By what mechanism does Faith lead to Salvation?

As I understand, Evangelical Protestants believe that Jesus took on the sins of humanity through his death, acting as a substitute for the target of the justice of God, and that salvation comes through faith in Jesus, as evidenced in the Gospels. Do Evangelicals have beliefs as to *why* (in a metaphysical sense) faith is required for salvation? If Jesus already took on the sins of the world, why are humans required to have faith in Jesus to be saved? FOR CLARITY: I understand it is stated in the Gospels that we must have faith to be saved, I am asking whether evangelicals have theories that explain why this is the case, or if it is simply accepted as a mystery.