Who did Cyrus defeat that allowed the followers of Yahweh to return to Jerusalem? What did the followers of Yahweh expect?

It was Babylon, The Euphrates River which was supposed to be protecting the outside of Babylon was diverted by Cyrus's army so that it would be dry enough for them to walk through to the open gates that were left open

It was Babylon, The Euphrates River which was supposed to be protecting the outside of Babylon was diverted by Cyrus's army so that it would be dry enough for them to walk through to the open gates that were left open because the Babylonians were Partying at the time and because of their carelessness most likely from being intoxicated they left them open which led to their siege.