The moment
Roman legions under Titus burned the Temple at the end of the revolt that had begun in 66 CE, ending sacrificial worship there. Synagogues, prayer and the study of Torah already existed and carried on. Rabbinic tradition remembers Yohanan ben Zakkai founding a school at Yavneh with Roman leave, and over the centuries that followed the rabbis' Judaism, rooted in the Pharisees, took shape.
People: Titus, Yohanan ben Zakkai