Among puzzlements of sitting down with JW reps with "What the Bible Really Teaches", was the assertion that Babylon was destroyed - forever - just like it says in these here chapters and verses. Then the NWT claims that Peter I & II were written from Babylon. But beside that, ancient Greek, Hebrew and Roman writings are full of reference to Babylon as an important center. Alexander the Great entered it in 331 BC - and eventually died there from fever caught on campaigns. He meant to make it his Capital.
Still with me on this? The first couple of books of Herodotus' Histories describes Babylon life in detail. These were written about a century after the unopposed entry of Cyrus into Babylon after defeating Babylonian armies farther afield. Xenophon and the 10,000 were headed there to serve as mercenaries in the late 5th century. And Alexander - well, when he wasn't chasing Darius III, apparently made a stopover there too.
How do we know? Well, for a start, did our ancestors seriously doubt the matter? A few days ago, I saw a notice in the papers about the work of a 17th century master: "Woven Gold: Tapestries of Louis IV at the Getty Center through May 1st". The illustration was the work of Charles Le Brun, a 16' x 26 foot tapestry titled, :Entry of Alexander into Babylon."
A search on line provided several more images. Additionally there were at least one film depiction (Oliver Stone's Alexander) and accounts of the event from classical writers, principally Roman writer Quintius Curtius Rufus (History of Alexander) and Greek writer Arrianis ( the Anabasis). Both evidently drew from earlier sources.
While the film Alexander sold well overseas, in the US, hardly anyone took note. Perhaps if I had seen the film, five years later I would had more to say to the JWs who would visit my house Saturdays trying to convince me that everything they had read or were required to quote from was incontrovertible and entirely true.