I suspect that a better understanding of how the Messiah's death saves us can be found by considering the story of the flood and Noah's ark. God's judgment was that our evil world should be destroyed, along with everything evil that is in it. The means of judgment was a worldwide flood. The ark was the only thing capable of going through and surviving the flood. Thus, anyone in the ark was saved.
If we apply that picture to the Messiah, then he was the only one who can go through the punishment of death and survive. Anyone "in" him will also go through death and survive. Thus, the Messiah had to suffer death and be raised from the dead, so that we can be united with him in death and likewise be raised with him to new life.
But how are we to be united with the Messiah? Is it only for those who believe in him? What about the rest of the world, who have never heard of him, or have been raised in a different religion? Are they to perish?
There is a difference of opinion among Christians about those questions. My own view is that those who are trying to live their lives by goodness and justice and mercy, are living by faith in the Messiah, who is the essence of goodness and justice and mercy, whether they know him personally or not. I suspect that they will find out that they were on the Ark the whole time.
Meanwhile, those who claim to believe in the Messiah, but do not try to live their lives by goodness and justice and mercy, will find out that they were never on the Ark.
Oh Lord, help us to live our lives by goodness, justice, and especially mercy, that you will be merciful to us on the last day.
ADDENDUM 2: If someone said to Noah, "I refuse to get on the Ark, but I try to live the right way," I don't think Noah would have been comfortable telling them they would survive the flood.