Jesus did not rebuild the temple.
Cyrus the Great.
After defeating Babylon, Cyrus the Great of Persia allowed the Jews (and other people) to return to their homeland in 538 BCE.
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, king of Persia.
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 return from exile predated Jesus by over five centuries.
Jews have returned to Jerusalem. However, there is no Jewish group seriously considering rebuilding the Temple as this would require destroying the Dome of the Rock Shrine of the Muslims and probably start a massive war.
King Solomon built the first Temple in 957 BCE with resources provided by his father King David. The second temple was allowed to be built by King Cyrus of Persia while the Jews were exiled in Babylon (536 BCE). Cyrus made a proclamation that the Temple in Jerusalem would be rebuilt, and the surviving Jews would return to rebuild it. This edict was supported by King Darius (522-486 BCE) who followed King Cyrus. This is described in the book of Ezra.
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.
The gentile ruler anointed by God was Cyrus the Great, king of Persia, who allowed the Jewish people to return to Jerusalem and rebuild their temple, fulfilling prophecies in the Old Testament.
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..