Sorry to burst your bubble, but the JWs don't deny this.
*** it-1 p. 237 Babylon ***
From that memorable date, 539 B.C.E., Babylon’s glory began to fade as the city declined. Twice it revolted against the Persian emperor Darius I (Hystaspis), and on the second occasion it was dismantled. A partially restored city rebelled against Xerxes I and was plundered. Alexander the Great intended to make Babylon his capital, but he suddenly died in 323 B.C.E. Nicator conquered the city in 312 B.C.E. and transported much of its material to the banks of the Tigris for use in building his new capital of Seleucia. However, the city and a settlement of Jews remained in early Christian times, giving the apostle Peter reason to visit Babylon, as noted in his letter. (1Pe 5:13) Inscriptions found there show that Babylon’s temple of Bel existed as late as 75 C.E. By the fourth century C.E. the city was in ruins, and eventually passed out of existence. It became nothing more than “piles of stones.”—Jer 51:37.