This has been a source of debate since the very earliest days of Christianity, but essentially the main idea isn’t that suffering in and of itself is what did it, it is that Jesus was a literal ritual sacrifice for the sins of humanity. In ancient Judaism, there was a lot of focus on animal sacrifices, and the Book of Leviticus lays out a very complex and rigid set of sacrifices that must be performed as atonements for each type of ritual impurity or sin, with the degree of sacrifice required roughly corresponding to the seriousness of the offense. It ranged from spiced cakes donated to the Temple for minor offenses to burning an entire bull without eating any of the meat for especially serious ones. Christians believe that by living a perfect human life and by being God incarnate, Jesus proved to be a good enough sacrifice to permanently atone for all the sins of humanity.

Of course, this begs the question of why God can’t decide he just doesn’t want to do all these sacrifices to begin with, and that goes back to Greek philosophers like Plato who tried to work out what properties a monotheistic God would have. One of the properties that got worked out was that if God is the greatest possible being, then He cannot change- after all, if He could, then he would have either not been the greatest possible being before, or he would be becoming something other than the greatest possible being. Therefore, if you believe that God created a set laws that demand sacrifice, then they must be in effect forever.

I would then wonder the validity of the assumption that the ancient Jewish laws were actually God’s divine laws in the first place under this set of assumptions, but that is assumed to be true by both Christians and Jews as a matter of faith.