Why would there be no law or no prophets without a temple? The first temple was destroyed. Yet the faith still continued.
“The Law and the Prophets were until John,” Jesus said (Lk 16:16). “Since then the good news of the kingdom of God is preached.”
The Baptist was the last of the Jewish prophets, really. He was the prophet upon whom the end of the age would alight. A few of the prophets had foretold their end, including Moses, but by the Baptist’s time, the end of the Jewish age was imminent, as was soon proved historically accurate as Judaism collapsed at the end of the Great Revolt and the Jewish people all but vanished by the end of the bar Kokhba Revolt.
Whatever prophecies Paul was alluding to in the churches matters not a whit to the Jewish eschatology, as the eschatology had already been established. And the Baptist was the last to utter it.
And the Law could not remain without the temple because the Law required temple-specific duties such as priestly ministrations, sacrifices, and pilgrimage festivals to the temple. In AD 70, the Law was impotent; the Sadducees couldn’t oversee it, and so the Pharisees couldn’t enforce it.
The time had come for the Jews to embrace the kingdom and start letting go of the temple, as they would have no choice but to let go of it in the latter part of AD 70. After the temple’s destruction in AD 70, no one followed the Law, and by the end of the bar Kokhba Revolt in AD 135, no one was left, really, who could have followed it even if they wanted to.