The Christian God is omnipotent, so couldn't He have forgiven humanity without all the horrible pain and suffering He sent his son through? The physical assention would have been enough to inspire the belief, and a global majority denies the resurrection was true, so that's not much motive.
There are several versions of the answer to this question, which is a very good one to ask.
The answer I would give is to do with what is called the Unequal Exchange. This is a situation where you have an immortal God, and a mortal creation. In particular he has a very special relationship with mankind, and wants to extend that relationship into eternity. But that relationship is threatened by man's propensity to cut himself away from relationship with God, and choose to behave in ways which God cannot look upon. It is this behaviour which is in some spiritual way connected with our mortality, and it is only by overcoming this life, and living without sin that death itself can be overcome.
God gives us eternal life by changing places with us. He takes on our humanity, and becomes man. Then he dies, and rises again from the dead. In doing this, he conquers the power of death for all time, and becomes the first born of a new creation; the first sinless man also becomes the first immortal man. Then all who believe in him are offered the same immortality that he has, because his holiness is infinite, and our sin - however bad - is finite. So all of our sin, which equates to separation, is burned away in the fire of his holiness, and nothing remains but love, and eternity.
This explanation leaves many questions unanswered, of course. Such as, why bother with all that; why not create men as immortal beings in the first place. I have no idea why not, except that the angels are immortal beings, and God created them, but clearly wanted to create mankind as well.
There is much that we do not know and struggle to understand. I personally do not think the manner of death was important, nor that it was the worst possible death, as some Christians try to claim. If they think that then they have very little knowledge of the extent of man's cruelty to man. What was important, imo, was the whole of the Incarnation, from start to finish, and the Resurrection. The tragedy of the crucifixion adds to the poignancy of the whole story, but it is the Unequal Exchange that is the heart of our faith.