Is it possible to reconcile Owen's trilemma with salvation by faith? John Owen's &quot;trilemma&quot; argument is often used as a defense for Limited Atonement, but it appears to have an underlying difficulty:

To which I may add this dilemma to our universalists: God imposed his
wrath, and Christ underwent the pains of hell, either for all the sins
of all men, or for all the sins of some men, or for some of the sins
of all men. ... If it was the first, then why are not all freed from
the punishment of all their sins? You will say, “Because of their
unbelief; they will not believe.” But this unbelief, is it a sin or
not? If not, why should they be punished for it? If it is, then Christ
either underwent the punishment for it, or he did not. If he did, then
why should that sin keep them from partaking of the fruit of his death
more than their other sins for which he died? If he did not undergo
the punishment for it, then he did not die for all their sins. (The
Death of Death in the Death of Christ [modernized edition by William
H. Gross], Book I, ch III)

He argues that Christ dying for sins means that unbelief (itself being a sin) should not prevent unbelievers from being saved. But if the atonement would save even those who never believe, then that seems to imply that faith is immaterial to salvation.
Is it possible to reconcile this line of reasoning with salvation by faith?
Clarification
To summarize the problem and the question:

Owen argues that Christ dying for a person means that unbelief would not stop that person from being saved, viz, &quot;...why should that sin keep them from partaking of the fruit of his death more than their other sins for which he died?&quot;

If, as Owen argues, the atonement means that unbelief doesn't disqualify someone from salvation, that seems to imply that faith makes no difference in whether one is saved.

The question then is how can faith making no difference in whether one is saved be reconciled with salvation by faith?
It is a fact, which is experienced and observed, that the unbelief of some does not exclude them from salvation, but their unbelief is overcome and they are saved from it :


  Afterward he appeared unto the eleven as they sat at meat, and upbraided them with their unbelief and hardness of heart. [Mark 16:14, KJV.]


It is a fact, which is experienced and observed, that some do not believe and they are left to themselves and they perish in their sins :


  And he [Judas] cast down the pieces of silver in the temple, and departed, and went and hanged himself.[Matthew 27:5, KJV.]


Thus it appears to be a fact, witnessed by observation and by experience, that salvation is of the Lord (Psalm 3:8, Psalm 62:1, Jonah 2:9) and that Jesus Christ died for the sins of a great multitude (bearing them in his own body on the tree, I Peter 2:24) - a multitude whom no man can number, Revelation 7:9, there being nothing at all 'limited' about this breath-taking atonement.

Thus it is also clear that salvation is by faith and clear that this faith is not derived from the self - it is God-given :


  For by grace are ye saved through faith; and that not of yourselves: it is the gift of God. [Ephesians 2:9, KJV.]


So it becomes clear, by observation, by experience, by divine revelation and by irrefutable logic, that the difference between the two aforesaid types of persons above, is not in and of themselves, but lies within the eternal Deity.


  So then it is not of him that willeth, nor of him that runneth, but of God that sheweth mercy.. [Romans 9:16, KJV.]


Which clear and plain truth is expressed by Dr Owen in his book 'The Death of Death in the Death of Christ' originally published in 1647.