According to Biblical Unitarians, Did Jesus know that he would succeed? Biblical Unitarians believe that Jesus was only a man and that he was given the gift of the holy spirit at his baptism in order to help him resist sinning and complete the purpose for which God the Father sent him.  As near as I can understand BU believe that Jesus had his own will which was sometimes different and even at odds with the will of God (for example, &quot;nevertheless not my will but your will be done&quot;).
I think BU would agree that God knew beforehand that Jesus would succeed as evidenced by the large quantity of prophecies given to that effect.  Here are just a couple of examples:

Behold, my servant shall act wisely; he shall be high and lifted up, and shall be exalted. As many were astonished at you— his appearance was so marred, beyond human semblance, and his form beyond that of the children of mankind— so shall he sprinkle many nations. Kings shall shut their mouths because of him, for that which has not been told them they see, and that which they have not heard they understand.- Isaiah 52:13-15


Yet it was the will of the LORD to crush him; he has put him to grief; when his soul makes an offering for guilt, he shall see his offspring; he shall prolong his days; the will of the LORD shall prosper in his hand. Out of the anguish of his soul he shall see and be satisfied; by his knowledge shall the righteous one, my servant, make many to be accounted righteous, and he shall bear their iniquities. - Isaiah 53:10-11

Jesus knew the Scriptures very, very well (to say the least) and he both knew what they said about God's Messiah and also that he was that very Messiah:

And the scroll of the prophet Isaiah was given to him. He unrolled the scroll and found the place where it was written, “The Spirit of the Lord is upon me, because he has anointed me to proclaim good news to the poor. He has sent me to proclaim liberty to the captives and recovering of sight to the blind, to set at liberty those who are oppressed, to proclaim the year of the Lord's favor.” 
And he rolled up the scroll and gave it back to the attendant and sat down. And the eyes of all in the synagogue were fixed on him. And he began to say to them, “Today this Scripture has been fulfilled in your hearing.” - Luke 4:17-21

He knew ahead of time that he would be handed over to the Gentiles by the Jews, mistreated, killed, and rise from the dead:

for he was teaching his disciples, saying to them, “The Son of Man is going to be delivered into the hands of men, and they will kill him. And when he is killed, after three days he will rise.” - Mark 9:31

In keeping with all of the Levitical prescriptions for sacrifices, the resurrection of Jesus from the dead is proof that he was successful in offering himself as a sacrifice without any spot or blemish of sin:

Great indeed, we confess, is the mystery of godliness: He was manifested in the flesh, vindicated by the Spirit, seen by angels, proclaimed among the nations, believed on in the world, taken up in glory. - 1 Timothy 3:16

I have seen BU content stating that Jesus, since he had a merely human will and was tempted in every way like we are, certainly could have sinned.
Given that Jesus knew he would justify many by rising from the dead and that this resurrection on our behalf required his death in a sinless condition:

Do Biblical Unitarians agree that Jesus must have known ahead of time that he would live a sinless life?

If yes, in what sense can it be said that Jesus &quot;could have&quot; sinned?
The scriptures are very clear - Jesus was a man tempted like us, made like us in every way.

Therefore he had to be made like his brothers in every respect... Heb 2:17

But the OP says Jesus is 'only a man'. No, not like any other man (which is what is implied), but a man without any sin. Yet he is still a man.
There is no room here for a God/man. A God/man is NOT like us in every respect.
We are given no rubbery descriptions of a man who 'gave up his Godliness' so that he could be tempted and die as a man, but who could not fail as God.
If Jesus could not sin, why the charade of being tempted his whole life? - not just in the garden or after his baptism - all his earthly days
What kind of game is God playing at, and the devil playing along too, (as he could never tempt God to sin) why would he bother humouring God with this temptation nonsense? He was up against a second Adam who would defeat him - not by being God, but by relying on God for success - hence the 40 days and 40 nights of fasting before this momentous temptation!
Lucifer wanted to avoid depending on God for his glory - he wanted to have it on his own terms - hence the rebellion. Jesus chose the humble and obedient route and the glory that could never be taken away. Not a glory taken by pride, but given in love and honour by the only true Glory Giver.

During the days of Jesus’ earthly life, he offered up prayers and petitions with loud cries and tears to the One who could--- save him from death---, and he was heard because of His reverence. 8 Although he was a son, he learned obedience from what he suffered. 9 And having been made perfect... Heb 5:7-9


Who is he praying to as God and why?
Can God die? No, nor can He be tempted by evil.
This is not about the cross - it references his whole life - at the very least after his baptism until the uttered words, 'it is finished'.

The son of God is plainly a man and a man plainly - except he began without sin.
Jesus says, without telling fibs,

you are looking for a way to kill me, a man who has told you the truth that I heard from God.

What games are we playing with the text to somehow read, 'God heard from God', or that saying he is a man means that he is also God?
He cannot be God for some purposes and not God for others. Pick one and let the text determine if it be true or not. This concept of Jesus being God renders only confusion and forces denial of basic scripture.
Simply being the fleshly mortal man that sprung from God's logos does not make him God. A simple word study of 'logos' will reveal that consistent reality throughout the NT. It does make him holy and without blemish - perfectly suited to be the one sacrifice for sin to redeem the mess begun with Adam. Yet he was still not qualified to be that sacrifice FOR sin.
He had to be made perfect or completed through suffering and the learned obedience that resulted. Does God need to learn obedience? Does God need to be made complete? No, but Jesus did. Because he had to suppress his will and submit to the Father - just as we do.
As God's logos, Jesus was God's word sent out to accomplish a task - a monumental task that only a man could do, and ONLY if he relied on God for all his needs.

So will My word be which goes out of My mouth; It will not return to Me empty, Without accomplishing what I desire, And without succeeding in the purpose for which I sent it. Isaiah 55:11

Jesus is the living word of God. He is not a predetermined outcome of a (silent) verbal decree from God. He has his own will that must be brought into submission. Not a static string of words, but a dynamic mortal life to accomplish what God had never done before.
When God sends His Holy Spirit into another vessel and 'fills that vessel', there is an increase in desire for God's will and purposes. God does not control that vessel, the vessel still has a will and can object, they still have to resist temptation to serve self. Paul, Peter, John tB, still had human nature that was ever-present. They are not perfect and still need saving. Satan doesn't go on holidays when God is around unless specifically ordered.  Jesus began without sin so didn't require salvation, but still had a human nature that could be influenced by the devil's tricks and subtle deceptions. While Jesus was well aware of these, he still had to resist and choose the Godly way. Clearly, sometimes this was more than difficult.
When Jesus asked for an alternative to 'the cup'(Matt 26:39) this was not God's doing, but Jesus fighting with the devils ploys to undo what had been a perfect run towards the cross.
Jesus knew he would succeed IF he relied on God, HIS God and Father.
This is the summation of what it is to be a Christian - what it is to be the Christ. God will succeed, He will have victory over evil, he will have His beloved creation redeemed!!!
But it will not be by force, decree or fiat, but by love and obedience. Humans think love and obedience are at odds - that is nonsense. That is the deception of what Satan has caused us to think about God and His son. Jesus showed us that it is true. He loved His Father and God and this led to obedience against ALL trial and suffering. Jesus' way would not work out, but God's way would. Jesus' will wasn't the way, God's will was.
We know little of Jesus life pre baptism. We know a lot about it after. If Jesus is God, is he somehow not God at moments of our random choosing? Is he God when he received the Holy Spirit? What was he before this, why is God being given the Holy Spirit?
All these and many more silly questions to force fit Jesus into a trinity dogma that the bible is eerily silent about. (sure there are some 'proof-texts&quot; that taken out of context or reliant on dodgy translations can lead to this kind of thinking, but they are readily understood as intended when the initial constraint of a threeology is removed)
Do Biblical Unitarians agree that Jesus must have known ahead of time that he would live a sinless life?
(I have not commented on the 'Jesus must have known ahead of time' phrase as I'm not sure what this means - what time?, what ahead? As Jesus did not literally pre-exist his conception/birth, any time before that is irrelevant regarding what he would 'know')
We see the OP quotes informing of a successful outcome. God's prophecies always come to fruition - in the way that He intended, at the time He intended, and through whom He intended.
We also know that Jesus prayed to be saved from death during his fleshly life because he could have sinned and fallen short of the perfection required. He tells us he had to surrender his will to the Father - if he had a differing will that needed surrendering, it was then capable of being at odds with God - therefore sin.
How did he manage this testing? Through prayer alone and total dependence of God- just like us. His example was of constant prayer, he exhorted  the disciples to have this attitude and practise Luke 18:1 and many others.
We are called Christians b/c we follow Christ. We are called to live as he lived, we are to behave as he did, to value the things he did. We cannot live as God lives on our own as God does. But we can follow His human son in his example of total dependence on God.  This idea is disingenuous at best - that God sends a son who cannot be beaten and expect us to fall in behind such a charade.
His prayers and his sweat like blood, were they a charade too? If he is God, it would be, as he could not fail and the whole son of God thing, with the sacrifice and the death and the resurrection was a huge farce.
In what sense can it be said that Jesus &quot;could have&quot; sinned?
Simply because he was a man and not God as the scriptures tell us via the NT and OT writers. There is no prophecy of God coming as a man. The seed of Abraham, the seed of the woman, the descendant of David.
God does not have a God, God does not need to be exalted to the place he already had or become heir to what he allegedly already made. Heb 1:2
Conclusion:
Jesus knew he could not sin to be the Lamb, he also knew he could if he let his guard down and thought his way was better, less painful, more expedient, than God's. The scriptures show this humble and fully reliant man on his Father and God as an example for all men to follow and become the brethren, of which he was the firstborn, to the new age of eternal life with God. Col 2:15, Rom 8:29

Now this is eternal life: that they know you, the only true God, and Jesus Christ, whom you have sent. John 17:3

Finally, God does not triumph over evil by trickery or deceit. He does not by force or supremacy over all, even the devil. He could have!
But no, He does so by love - the love He has for all and the love that He places within us by His spirit - just as He did with His son Jesus. Jesus loved back by the presence of God's spirit and nature.
There is no deception, He says what is, and we must read what is written - without making stuff up or reading what we want it to say. If we are told Jesus is a man, then a man he is - how then can he be God too? Why should we try to make him so against the scriptures?
This answer is gleaned from https://www.biblicalunitarian.com/