We do not need to understand how God placed our sins upon Christ or how precisely Christ took the penalty for us, bearing our punishment, but we can be sure that he did. In the natural world, geologists do not understand (or at least have not agreed upon) plate tectonics and physicists are unsure how light refraction works, but there is no question that the earth’s movements cause earthquakes or that light bounces off the chrome bumpers of cars. Knowing how something occurs and knowing that something occurs are not the same thing. The former is not required for the latter. Faith does not require all of the mechanics of knowing before we can believe that something is true.
God made him who had no sin to be sin for us, so that in him we might become the righteousness of God.
2 Cor. 5:21
He himself bore our sins in his body on the tree.
1 Pt. 2:24
Surely he took up our infirmities
and carried our sorrows,
yet we considered him stricken by God,
smitten by him, and afflicted.
But he was pierced for our transgressions,
he was crushed for our iniquities;
the punishment that brought us peace was upon him,
and by his wounds we are healed.
We all, like sheep, have gone astray,
each of us has turned to his own way;
and the LORD has laid on him
the iniquity of us all.
He was oppressed and afflicted,
yet he did not open his mouth;
he was led like a lamb to the slaughter,
and as a sheep before her shearers is silent,
so he did not open his mouth.