All branches of Protestantism, be they 'Evangelical' or not, ought to agree that faith in the resurrected Jesus Christ is essential for salvation. I have included the word 'resurrected' because it is faith that, not only did he die for sins, but was resurrected (due to having died without having sinned himself) that means he is still alive. Therefore, Christians do not have faith in a dead Jesus; it is the power of his resurrection that 'enables' salvation to come to repentant sinners.
You asked what 'the mechanism' is for faith leading to salvation, and fortunately for all who believe the Bible to be God's inspired word, the explanation is given there. Let this Reformed Protestant scholar explain in his book. First, he sets before us the reality of the horrific offense of the cross of Christ, for if this is not faced up to squarely at the outset, we will not awaken to why it was necessary, and what Christ's death on it accomplished for sinners:
"The impression is often given that the evangelical understanding of
the cross, our doctrine of the atonement, somehow increases the pain
of the Saviour. But it is not a theory that constitutes the pain of
Christ. The pain was in the facts: that on the cross he suffered in
body, suffered in soul, suffered from Heaven and from earth and from
Hell. The fact is, Christ died. The fact is, He paid the wages of sin.
The fact is, He was dealt with as sin deserved. There are three
further facts that accentuate this central fact of the suffering of
First, His sinlessness...Secondly, the One who receives the wages of
sin is the Son of God... The third twist in the paradox is that the
cross is the act of God the Father: 'God so loved the world, that he
gave his only begotten Son' (John 3:16). He did not spare His own Son
but delivered Him up for us [believers] all (Romans 8:32)...
We really must learn to see the cross as a gigantic problem, a problem
of mind-boggling proportions. We must see the scandal of it. We must
say, 'What is this ugliness? What is this blot on the moral universe?
What is this when God the Father is crucifying His own Son, when the
righteous God is exacting from the Sinless one the wages of sin? What
is this horrendous anomaly, this thing that we cannot understand, this
offense, this hateful, wretched, ugly thing?'...
What is the New Testament solution to the problem? It is this: that
the death of Christ was a sacrifice. It was not an accident. It was
not an act of divine malice...
But what did it mean for Christ to be a sacrifice: to be the 'lamb
without blemish and without spot' (1 Peter 1:19)? It meant that He was
the One to whom sin was imputed... But sin
was such, the offence against God such, the depravity such, the guilt
such, that the salvation could not be completed until Christ had...
endued what our sin deserved. The Son of man came 'to give his life a
ransom for many' (Matthew 20:28; Mark 10:45). He was 'obedient unto
death' (Philippians 2:8)... And what is death? It is the penalty for
sin!" A Faith To Live By, Donald Macleod, pp. 131-135 Mentor, 1998
It is who we need to put faith in, and in what he accomplished for us, that matters, if we are to be saved. It is not just an abstract something - 'faith' - as if it is a quality that enables people to say, "Oh, yes, I have faith!" Much that passes for evangelical Christianity has tried to sanitize the cross of Christ, to gloss over it quickly in order to dwell on the niceness of the prospect of Heaven. But unless we know what was achieved on that cruel cross, and why that had to be done - for us sinners - we will have a shallow view of salvation due to having a shallow view of sin, and a superficial awareness of spiritual need. We need to begin to grasp the depth of our own depravity and the extent of our own guilt to truly appreciate God's provision in the blood of His Son.
'God has reconciled us to himself by Jesus Christ... For he has made him to be sin for us, who knew no sin, that we might be made the righteousness of God in him.' (2 Corinthians 5:18-21) And because he had no sin, death could not hold him. He arose in triumph over sin, death, and hell. That is the 'mechanism' of God's salvation in Christ. That is what, and who, we have to utterly trust - and to have faith in nothing, or no-one else for salvation. We cannot have faith in any religious systems, or in any creeds, or in any rituals, as if diligence in those respects will merit us God's salvation. We cannot contribute to the finished work of Christ on the cross. He did it all. If that doesn't get us down on our knees in repentant faith, nothing else will.
That is why it is vital to see that scripture states that Christ suffered for the sins of his people. There is no 'universal salvation' just requiring individuals to complete the work by their choice, their agreement. We must be clear why works cannot possibly save and why salvation is dependent upon faith in the finished work of Christ. This is the wonder of the cross.