The beginning of the Fourth Gospel tells us that it was Jesus, The Word, who made this world; and it is this work of creation which enabled Jesus (and only Jesus) to be our saviour.
Having made this world; Jesus was then incarnated-into the world he had created; that is, he was incarnated from his creation, using the stuff of his own creation. This world has that primal and fundamental unity - of being created by Jesus - everything is inter-related and mutually-affecting, by kinship of shared origin.
So we too are all incarnated from this world, from the creation of Jesus.
When Jesus died and was resurrected; this was the death and resurrection of the creator of this world, Jesus's mortal body and his resurrected body were both of this world (which Jesus himself had made).
We are incarnate from this world, Jesus became incarnate from this world (which he had made); we and Jesus are both Men; and therefore Jesus's death and resurrection had universal significance for Men.
This it was, that made it possible for other Men to follow Jesus into resurrected life everlasting; and why only Jesus is our saviour.
Why then do we need to have faith in Jesus? Why doesn't salvation just-happen?
Because there are two things Jesus gave us; the first is 'physical' resurrection to eternal life, the second is 'dwelling' in Heaven (life 'everlasting', and life qualitatively greater - not merely unending existence...).
Resurrection just-happens, and it happens to all men. Instead of remaining as a severed soul - as was the case for all Men before Jesus; since the resurrection of Jesus, all Men (including those from before the time of Jesus) are resurrected.
Resurrection is not a choice - it 'just happens' - it is something like a change in physical reality; a change in what happens to the soul after death.
But Heaven is a choice, a decision, an act, an opt-in - and salvation therefore happens only through faith - that is love, trust of Jesus.
To understand this requires recalling the fate of the soul after the death of the body, and before the resurrection of Jesus - the soul was a witless, demented thing of little intelligence, little memory, little judgement, no free will... incapable of helping itself...
(This, at least, is how both the ancient Hebrews (with Sheol) and ancient Greeks (with Hades) regarded life after death - and other variants may be understood similarly. The soul after death was a damaged, incomplete, incapable thing - eternal life was merely eternal existence.)
I regard the Good Shepherd parable as providing the key to understanding salvation - which is that while the soul is always resurrected, resurrected Man cannot find his own way to Heaven.
The resurrected soul must be led to Heaven; that is, Man must choose to follow the guidance of the Good Shepherd. This following is not imposed, it is chosen.
This was made newly possible by Jesus because the resurrected soul has greater capability than the discarnate souls destined for Sheol/ Hades; the resurrected soul has sufficient capability to recognise Jesus, to know him; it has the capacity and necessity to choose whether to follow the Good Shepherd, or not.
Why would the resurrected soul follow the Good Shepherd to Heaven, except that the soul loved and trusted the Good Shepherd?
That is the need for faith.
Thus Jesus was necessary to our salvation, only Jesus could give us salvation, only faith in Jesus can lead us to salvation.