Read my post again. The a Greek King could have had the Babylonians to manufacture it for him.
The problem with that is, the Greeks were known for building gizmos and doodads of all kinds, as well as fine work found all over Europe from that time, and into Roman times (some of Julius Caesar’s opponents among the Gauls and Germans even used Greek-style phalanx tactics and weapons). Whatever skills were in Babylon seem to have been Greeks (because they were well-distributed across the Persian Empire even in Alexander’s time) or Jews (renowned for working with silver and gold).