Judaism after the Second Temple, what happened?

I’ve been learning about the history of Jews and Judaism, and I have a question. I’m not Jewish, so hopefully I’m not saying anything dumb. 🙂

When the Second Temple was destroyed, how did the Jewish people rationalize the subsequent changes to the practice of Judaism? If the Temple was holy, then wouldn’t Judaism not be itself without it? What was the thinking that allowed Judaism to evolve so fundamentally?