Alternative Pasts

If the past had been very different from the way we think it was, then time travelers would discover this. Julian May's time travelers discover that malign aliens ruled Earth in the Pliocene. (Both May and Poul Anderson describe the Atlantic pouring into the Mediterranean.) Other theoretical possibilities are:

if Biblical Fundamentalism were literally true;
if aliens really built the Pyramids;
if the Greek gods really ruled Earth from Olympus;
if SM Stirling's Empire of Shadow had really existed.

Poul Anderson's Time Patrol Specialists do not discover, e.g., that there really was a city of Ys, inundated by the sea god, Lir, but, of course, someone could write a fantasy/sf synthesis in which that is what happened.

Technological time travelers from an actual or potential future would complicate the wars of the gods and such concepts are usually kept apart. However, combining two discordant ideas might generate a third and novel idea. Where do ideas come from?