Would you or anyone you know willingly, knowingly worship any god they know doesn't exist?
No, right?
Neither would the Israelite on the old days.
(At times) They worshipped multiple gods, and they believed all of them to be real, or they wouldn't have worshipped them.
Which means the Bible shows us that the Israelites didn't really see a difference in the actual existence between Jhwh and other gods. They were all equally real to them. They allegedly had plenty of evidence of JHWH being real, and that evidence was apparently no better than the evidence they had for other gods being real.
In the Bible false god doesn't mean not existing god as we are now taught. It means not our preferred god Jhwh.
The Israelites were polytheistic, and then chose to worship only one of those gods.