King Nebuchadnezzar, King of Babylon, captured Judah in 606 B.C. (probably just before 605 B.C.), which is discerned from Daniel 1:1 and Jeremiah 25:1. At that time some people from the royal family and from the “nobility” were forced to leave Judah and to enter exile in Babylon. That was the first wave, albeit a small captivity, of exiles.
The second wave of Jewish people forced to go to Babylon was in 597 B.C., which is learned from 2 Kings 24:12-14. That was the largest group brought to Babylon! Then in 586 B.C., after a siege in the wake of the King of Judea, Zedekiah, rebelling against Nebuchadnezzar, Jerusalem was destroyed, the Temple was burned, and a final group of Jewish people were brought as exiles to Babylon, which is told in 2 Kings 25:1-12.
So even though Jerusalem was not destroyed until 586 B.C., there had been Israelites taken captive to Babylon eleven years before and twenty years before, thus Jeremiah’s prophecy was right on.
It is my opinion the odds were zero the Jewish people would ever again be able to go home. Yet in 536 B.C., King Cyrus of Persia captured Babylon. (A number of modern scholars say it was 539 B.C., contradicting numerous scholars from the entire 20th century without solid evidence.) This is learned from Ezra 1:1-4. (You can also get details about this capture from Herodotus the historian from the 5th century. And Herodotus records how Babylon was a tough country not only to conquer, but to hold, since they even broke away at least once for a short period of time under Persian rule.) Then King Cyrus allowed the Jewish people to go home. I think it was a miracle.
Hunter Irvine