Yes. In 539 BCE, King Cyrus the Great of Persia gave permission for the Jews of Babylon to return to their ancestral homeland and rebuild the Temple.
This is a sentence, not a question. If you meant to ask "Did the Israelites return and rebuild the temple?" or you meant to ask "Will the Israelites return and rebuild the temple?", see the two Related Questions below.
The Persian king Cyrus after he defeated the Babylonians, released the Israelites who were taken prisoners by the Assyrians He allowed them to take the temple vessels and helped rebuild the destroyed temple..
It meant that the Israelites could once again have independence, return to their land and rebuild the Temple. And it showed how the relevant prophecies were fulfilled exactly.
Jesus did not rebuild the temple.
There was no 'church' and Israel was in northern Palestine. Hebrews who had been deported to Babylon by the Babylonians were allowed to return to Jerusalem to attempt to reclaim ancestral lands, and on the side rebuilt the destroyed temple.
Cyrus the Great.
The Jews of the Babylonian Exile were granted the right to return to the Land of Israel, and rebuild the Temple which had been destroyed by Nebuhadnetzer.
About 40,000 of them returned to the Holy Land and built the Second Temple. The rest remained in Babylonia and their other places of exile.
The tradition is that it was Cyrus the Great, king of Persia. Additionally: King Cyrus of Persia made a decree allowing the Jewish exiles to return to Jerusalem to rebuild the Temple. The construction of the Temple continued under King Darius and was completed in 516 BCE. (Ezra 6:15).
He made a proclamation inviting the Jews to return to Israel (Judea) and rebuild Solomon's Temple under Ezra. This made the Second Temple Era possible.
About 40,000 of the Hebrews aristocracy who had been deported to Babylon and were willing to return and try to recover land they claimed in Judah.
Because of his tolerant attitude, Cyrus permitted the Jews to return to Israel (Judea) and rebuild the Temple.