A few details you overlooked.

The best evidence indicates that the "old testament" was created shortly after the return of the Babylonian Captives. Thus, they had been quite thoroughly exposed to the Epic of Gilgamesh, And Zorastarnism, with it's Supreme Deity Ahura Mazda, and his adversary Ahriman. Additionally, there is very little evidence of Saul, David, or Solomon in actual archaeological evidence.

It likely appears to be that "King" Josiah, the "rebuilder" of the "Temple of Solomon" needed to create a national identity for the tribe of refugees returning from Babylon, and the "discovered" "Ancient Documents" in the "Temple Ruins" probably didn't even have dry ink yet. He had his priests compile a "holy book" out of whatever myths and legends they knew to support his "Supreme God YHVH" and it went downhill from there.

And, there is every reason to think that exact same thing happened 500 some odd years later, under Peter and Paul, since there is even less actual evidence to Yeshua Ben Yosef's existence. (At least we have ONE pottery shard with "house of David" inscribed on it.)