What is an overview of Christian viewpoints on the eternal destiny of individuals who die never hearing the Gospel? Many individuals die never having heard the Gospel. Some illustrative examples are: pretty much everyone who was born before Jesus, individuals contemporary to Jesus but who were too far away at the time to hear about him (e.g. Native Americans and all tribes from the Pre-Columbian era during the first and many subsequent centuries), isolated jungle tribes in Africa and the Amazon, and uncontacted peoples in general.
How do different denominations across Christianity view the problem of individuals dying without ever having heard the Gospel's salvation message? What is the biblical basis in each case?
Note that this is an overview question: answers must summarise the positions of several different major Christian branches, and if possible even some of the smaller ones as well.
What is an overview of Christian viewpoints on the eternal destiny of individuals who die never hearing the Gospel?
Many peoples have as yet not been evangelized and are considered uncontacted people!
At first glance, this question is basically straight forward, but it does not address the question of infant baptism or infants that die without the grace of baptism or the souls that died prior to Our Lord’s  first coming. I think that these souls should also be included in those souls who die never hearing the Gospel.
Catholicism
To all of the Catholicism believes that salvation is possible in some circumstances.

Issue:
What does the Catholic Church mean by the phrase, &quot;Outside the Church there is no salvation&quot; (extra ecclesiam nulla salus)?
Response:
All salvation comes through Jesus Christ, the one Savior of the world (cf. Acts 4:12). His Holy Spirit dispenses those graces through His body, the Church. &quot;He who hears you hears me, and he who rejects you rejects me, and he who rejects me rejects him who sent me&quot; (Lk. 10:16).
Response:
All salvation comes through Jesus Christ, the one Savior of the world (cf. Acts 4:12). His Holy Spirit dispenses those graces through His body, the Church. &quot;He who hears you hears me, and he who rejects you rejects me, and he who rejects me rejects him who sent me&quot; (Lk. 10:16).
Quoting from various documents of Vatican II and Pope Paul VI, the Catechism of the Catholic Church (no. 776) explains:
As sacrament, the Church is Christs instrument. She is taken up by Him also as the instrument for the salvation of all, the universal sacrament of salvation, by which Christ is at once manifesting and actualizing the mystery of Gods love for men. The Church is the visible plan of Gods love for humanity, because God desires that the whole human race may become one People of God, form one Body of Christ, and be built up into one Temple of the Holy Spirit. Discussion: There are two principal errors when it comes to the Churchs teaching on extra ecclesiam nulla salus. Some reject this teaching as both incorrect and arrogant. Others interpret this statement to condemn all those who are not visibly united to the Roman Catholic Church. To properly understand this teaching, we must examine it within the context of divine Revelation and Church history. This examination will reveal that the phrase was not formulated to express who would go to heaven and who would go to hell, for only God will judge that. Rather, the phrase expresses an understanding of the Church in relation to her role in the salvation of the world.
Quoting from various documents of Vatican II and Pope Paul VI, the Catechism of the Catholic Church (no. 776) explains:
As sacrament, the Church is Christs instrument. She is taken up by Him also as the instrument for the salvation of all, the universal sacrament of salvation, by which Christ is at once manifesting and actualizing the mystery of Gods love for men. The Church is the visible plan of Gods love for humanity, because God desires that the whole human race may become one People of God, form one Body of Christ, and be built up into one Temple of the Holy Spirit. Discussion: There are two principal errors when it comes to the Churchs teaching on extra ecclesiam nulla salus. Some reject this teaching as both incorrect and arrogant. Others interpret this statement to condemn all those who are not visibly united to the Roman Catholic Church. To properly understand this teaching, we must examine it within the context of divine Revelation and Church history. This examination will reveal that the phrase was not formulated to express who would go to heaven and who would go to hell, for only God will judge that. Rather, the phrase expresses an understanding of the Church in relation to her role in the salvation of the world.
Translation or Interpretation?
Many people translate the Latin phrase extra ecclesiam nulla salus as &quot;Outside the Church there is no salvation.&quot; This translation does not seem entirely faithful to the Latin meaning, and contributes to the misunderstanding of the phrase.
The Latin word &quot;extra&quot; is both an adverb and preposition. Depending on its use in a sentence, the word has different meanings. When used to describe spatial relations between objects, the word is translated as &quot;beyond&quot; or &quot;outside of&quot; (e.g., Beyond the creek is a tree; or, James is outside of the room). When used to describe abstract relations between concepts or intangible things, the word is commonly translated &quot;without&quot; (e.g., Without a method, it is difficult to teach). Within the phrase in question, extra is a preposition describing the abstract relationship of the Church to salvation. Considering the Latin nuances of the word, a proper translation would be, &quot;Without the Church there is no salvation.&quot; This translation more accurately reflects the doctrinal meaning of the phrase.
Scriptural Foundations
In the Gospel of Mark, after the Resurrection, Jesus appeared to the Eleven and gave them the commission, &quot;Go into all the world and preach the Gospel to the whole creation. He who believes and is baptized will be saved; but he who does not believe will be condemned&quot; (Mk. 16:15-16).
In order to accept or reject the Gospel, each person must have it preached to him. If acceptance or rejection of the truth were based on private revelations given to each man, woman, and child, there would be no need for Christ to commission the Apostles to preach the Gospel. Jesus desired to reveal Himself through His body, the Church. While this passage condemns those who reject the truth, it does not condemn those who have not had the truth offered to them as Christ intends.
The New Testament clearly teaches that salvation is a gift offered by God in various ways to all men. Adam, Abel, and Enoch lived between the first sin and the covenant of Noah. They were bound by original sin. All are considered to be in heaven. Enoch did not even die, but was taken to God before death (Heb. 11:4-5). These men were neither baptized nor circumcised, but nonetheless saved.
When the gentile centurion came to Jesus in Capernaum and asked for the healing of his servant, Our Lord agreed to go to his home, but the centurion said, &quot;Lord, I am not worthy to have you come under my roof; but only say the word, and my servant will be healed&quot; (Mt. 8:8). Jesus replied:
&quot;Truly, I say to you, not even in Israel have I found such faith. I tell you, many will come from East and West and sit at table with Abraham, Isaac, and Jacob in the kingdom of heaven, while the sons of the kingdom will be thrown into the outer darkness; there men will weep and gnash their teeth&quot; (Mt. 8:10-13).
Jesus makes a clear distinction between those who are sons of the kingdom (that is, those who have knowledge of and accepted the faith) and those who are not. He includes in the kingdom of heaven many of those who are not. Jesus graces us with His incarnation, and His presence is known through His body, the Church. The Church carries on the work of Christ here on earth. Those to whom the Church has not preached the Good News will be judged by God in a manner known to God and tempered with His mercy. As St. Paul explains:
&quot;When Gentiles who have not the law do by nature what the law requires, they are a law to themselves, even though they do not have the law. They show that what the law requires is written on their hearts, while their conscience also bears witness and their conflicting thoughts accuse or perhaps excuse them on the day when, according to my Gospel, God judges the secrets of men by Christ Jesus&quot; (Rom. 2:14-16).

The Catechism of the Catholic Church is very clear on this issue:

&quot;Outside the Church there is no salvation&quot;
846 How are we to understand this affirmation, often repeated by the Church Fathers?335 Re-formulated positively, it means that all salvation comes from Christ the Head through the Church which is his Body:
Basing itself on Scripture and Tradition, the Council teaches that the Church, a pilgrim now on earth, is necessary for salvation: the one Christ is the mediator and the way of salvation; he is present to us in his body which is the Church. He himself explicitly asserted the necessity of faith and Baptism, and thereby affirmed at the same time the necessity of the Church which men enter through Baptism as through a door. Hence they could not be saved who, knowing that the Catholic Church was founded as necessary by God through Christ, would refuse either to enter it or to remain in it.336
847 This affirmation is not aimed at those who, through no fault of their own, do not know Christ and his Church:
Those who, through no fault of their own, do not know the Gospel of Christ or his Church, but who nevertheless seek God with a sincere heart, and, moved by grace, try in their actions to do his will as they know it through the dictates of their conscience - those too may achieve eternal salvation.
848 &quot;Although in ways known to himself God can lead those who, through no fault of their own, are ignorant of the Gospel, to that faith without which it is impossible to please him, the Church still has the obligation and also the sacred right to evangelize all men.&quot;

Infants are incapable of belief, yet the door of salvation may still be open to them.
Very few Greek Fathers dealt with the destiny of infants who die without Baptism because there was no controversy about this issue in the East. Furthermore, they had a different view of the present condition of humanity. For the Greek Fathers, as the consequence of Adam's sin, human beings inherited corruption, possibility, and mortality, from which they could be restored by a process of deification made possible through the redemptive work of Christ. The entrusts infants born without baptism to the mercy of God.

1261 As regards children who have died without Baptism, the Church can only entrust them to the mercy of God, as she does in her funeral rites for them. Indeed, the great mercy of God who desires that all men should be saved, and Jesus' tenderness toward children which caused him to say: &quot;Let the children come to me, do not hinder them,&quot;64 allow us to hope that there is a way of salvation for children who have died without Baptism. All the more urgent is the Church's call not to prevent little children coming to Christ through the gift of holy Baptism.

As regards the Christian theology about the fate of the unevangelized, there seems to be basically four possible solutions amongst believers. However, some of these positions are fraught with serious biblical and theological challenges.

Views on the Unevangelized

Universalism: This is the view that God will ultimately save all people through Christ’s sacrifice regardless of whether they believed, disbelieved, or had never heard the explicit gospel message itself.

Also called universal salvation, this position reflects what might be defined as an extreme optimism concerning the redemptive grace of God. Its defenders, though always a minority in church history,1 nevertheless insist that various biblical verses can be understood to support this viewpoint.
Universalism has been described, at minimum, as a “revisionist challenge to orthodoxy” (including Eastern Orthodox, Roman Catholic, and Protestant) because a version of the teaching was condemned as a heresy in church history.3 Historic Christian orthodoxy has rejected universalism because Scripture indicates that some peoplewill suffer eternal divine judgment because they have rejectedGod and specifically Jesus Christ as Lord and Savior (for example, Matthew 25:32–33, 41, 46; John 3:36; Revelation 14:11).

Inclusivism: This view holds that people (among other religions and among the unevangelized) can be saved by responding favorably to God even if they have never heard of Christ. The Catholic theology of the Second Vatican Council (1962-65) said people of good will who never hear of Christ could be saved by Christ as “anonymous Christians.”4 Thus, the unevangelized are not excluded merely because they have never heard the gospel. However, this view has been rejected by many traditional Christians because it fails to recognize the depth of sin’s bondage on the human will and the potential idolatrous thinking of non-Christians. Also, Scripture clearly teaches that salvation comes through hearing the explicit preached Word (Romans 10:17).

Exclusivism: This position is the traditional Christian view. It asserts that the unevangelized are apparently lost apart from hearing and responding affirmatively to the gospel message because they have sinned in Adam. Therefore, theyhave no right to divine grace but will be judged by the general revelation God has given to all human beings. At this point of tension, exclusivism must account for the Jews and holy pagans who were saved in the Old Testament before hearing about the explicit message of Jesus Christ. Moreover, there appear to be three versions of exclusivism:5


Restrictive exclusivism affirms that conscious faith in Christ is necessary for salvation and therefore the unevangelized are definitely lost.
Pessimistic exclusivism affirms that while the fate of the unevangelized is not known with certainty, there is no clear evidence in Scripture that God will perform an extraordinary work of grace to reach the unevangelized apart from the normal means of the preached gospel. So the unevangelized are likely lost.
Nonrestrictive (optimistic) exclusivism affirms that while the fate of the unevangelized is not known, Scripture seems to indicate that God may reach out to those who haven’t heard the gospel in some extraordinary way (dreams, after-death tests, etc.).

Agnosticism: On this view humans can not definitively know the state of the unevangelized and their fate is God’s prerogative.

Protestant interpretation
The doctrine is upheld by many in the Protestant tradition. Martin Luther, the foremost leader of the Protestant Reformation, spoke of the necessity of belonging to the church (in the sense of what he saw as the true church) in order to be saved:

Therefore he who would find Christ must first find the Church. How should we know where Christ and his faith were, if we did not know where his believers are? And he who would know anything of Christ must not trust himself nor build a bridge to heaven by his own reason; but he must go to the Church, attend and ask her. Now the Church is not wood and stone, but the company of believing people; one must hold to them, and see how they believe, live and teach; they surely have Christ in their midst. For outside of the Christian church there is no truth, no Christ, no salvation.

The Genevan reformer John Calvin, in his Reformation-era work Institutes of the Christian Religion, wrote: &quot;beyond the pale of the Church no forgiveness of sins, no salvation, can be hoped for&quot;. Calvin wrote also that &quot;those to whom He is a Father, the Church must also be a mother,&quot; echoing the words of the originator of the Latin phrase himself, Cyprian: &quot;He can no longer have God for his Father who has not the Church for his mother.&quot;
Reformed scholastics accepted the phrase so long as the church is recognized by the marks of the church, which they defined as proper administration of the Word and sacrament, rather than apostolic succession.
The idea is further affirmed in the Westminster Confession of Faith of 1647 that &quot;the visible Church ... is the Kingdom of the Lord Jesus Christ, the house and family of God, out of which there is no ordinary possibility of salvation.&quot; Despite this, it is not necessarily a commonly held belief within modern Protestantism, especially within evangelicalism and those denominations that believe in the autonomy of the local church. The dogma is related to the universal Protestant dogma that the church is the body of all believers, and debates within Protestantism usually center on the meaning of &quot;church&quot; (ecclesiam) and &quot;apart&quot; (extra). - Extra Ecclesiam nulla salus

Orthodoxy
For the Orthodox, the question is in God’s hands and thus is an open question.

Regarding God’s mysterious work outside the Orthodox Church, we have nothing to say. We make no judgments about what God is doing there, or about what happens to the souls of those who are not Orthodox or not Christian on earth. It is all we can do to try to “work out [our] own salvation with fear and trembling” (Philippians 2:12). - Do All Non-Orthodox People Go to Hell?

Anglicanism

The idea is further affirmed in the Westminster Confession of Faith of 1647 that &quot;the visible Church ... is the Kingdom of the Lord Jesus Christ, the house and family of God, out of which there is no ordinary possibility of salvation.&quot; Despite this, it is not necessarily a commonly held belief within modern Protestantism, especially within evangelicalism and those denominations that believe in the autonomy of the local church. The dogma is related to the universal Protestant dogma that the church is the body of all believers, and debates within Protestantism usually center on the meaning of &quot;church&quot; (ecclesiam) and &quot;apart&quot; (extra).

Thus extraordinary means of salvation would be at God’s disposal.
The Church of Jesus Christ of Latter-Day Saints
Notable because baptism is seen as necessary for salvation, but individuals who die never hearing the gospel are not automatically condemned since before the Final Judgement / Resurrection, there is still opportunity in the after-life for hearing the gospel, accepting Christ, and receiving baptism by proxy.

Does everyone need to be baptized? Yes. Jesus made it clear that being
born of water and of the Spirit is necessary to enter the kingdom of
heaven (see John 3:1–13).
What happens to people who die without baptism? God has provided a way
for everyone to receive all of His blessings—even after death.
Baptisms and other essential ordinances can be performed on behalf of
those who have died without the opportunity. The Apostle Paul spoke of
baptism for the dead in the Bible (see 1 Corinthians 15:29) and
members of The Church of Jesus Christ of Latter-day Saints continue
that same practice in temples today.
Here’s how it works: Latter-day Saints study their family history to
discover names of people who have died without being baptized. Members
are then baptized on behalf of those ancestors in the temple. This
service for others is offered in love—and because life continues after
death, those who have died are aware of the ordinances and can choose
whether or not to accept them. Common questions

All in all it seems rather interesting that many denominations hold that they hold as saints those who are mentioned in Sacred Scriptures (Bible) as being a saint and thus saved, yet did not know Jesus Christ on a personal level!
Many Old Testament Figures are recognized a saints in various denominations. Obviously, they could not have believed in the Gospels of Jesus Christ.
When we enter eternity, there will be many surprises.