The Medes already "destroyed" Babylon. They conquered it, destroying its freedom & independence. But the city itself existed for several hundred more years as an unimportant town that was slowly being abandoned. It still existed when Jesus was here.
But GOD said it would never be rebuilt. Look at what happened to Saddam Hussein for trying to rebuild it. Two of his sone died in it, & the USA used his buildings there for artillery practice.
The NEW Babylon that'll be swiftly destroyed is lakely Rome, Italy. Please read Rev. 17 CLOSELY to see if this doesn't describe Rome and the Vatican. They'll try to control the "man of sin", but he will turn on them when their usefulness to him is over.