I think the real cultural memory of the Neanderthals and other species related to us is in the myths of Titans and Giants. People who were on earth first and who battled furiously with man-like gods for dominance.
The story of who a person was can easily be a combination of many.
This all to say that the word (and the sacred culture attendant) is far older and far broader than can be ascribed to some just-so story of a prehistoric, let alone proto-Greek, warlord. If I were to look for origins of “Zeus,” the god, I would instead first contemplate how vast the sky appears when seen from the steppe (whence the Yamnaya, first speakers of this language family). How does one not imagine a sky father in that seeming infinity?