scholar:
The only suitable candidate in answer to your question is the Fall of Babylon in 539 BCE. This date is well cinfirmed by secular chronology and is well documented in the Bible.
It's funny how 'scholar' is happy to agree that 539 is "well cinfirmed by secular chronology", yet he at the same time rejects other dates that are even more strongly confirmed by secular chronology, including the siege against Jerusalem by Nebuchadnezzar from late 598 until early 597, which is in turn inextricably linked to the overlapping periods of reign of Babylonian, Egyptian and Persian rulers.
The Bible is in complete agreement with what is known in secular history that Nebuchadnezzar demanded tribute from Jehoiakim in early 604 which he then paid for 3 years; that Nebuchadnezzar lost a battle against Necho in 601 resulting in Jehoiakim then refusing to pay tribute; that Nebuchadnezzar sent various marauder bands against Judea in 599 while he remained in Babylon to muster his own army; that Nebuchadnezzar besieged Jerusalem in late 598 and took most of its people into exile; and that Jerusalem was subsequently destroyed in 587.
InChristAlone:
I think 537 was an assumption that it took a couple years for the Israelites to return and is really meaningless.
It can be called an assumption. (The most definite that Insight is willing to be about 537 is that it is allegedly "very probable".) More accurately, it's a lie. The Watch Tower Society used to say the Jews returned in 536BCE. When they learned (in 1943) there was no year 0, they changed it to 537 so they could shift 606 to 607 in order to maintain their superstitious beliefs about 1914. The false claim about 537 is disproved by comparing what is stated by Josephus and Ezra. The Jews who returned were in Judea by Tishri (September/Octobe) of 538 BCE.