fully incorporated into the fascist mythology
True, fascist mythology is to a big degree about projecting a golden thread through history. The Germanic people for example do not have a coherent history as the Nazis made it look like. By saying that the narrative is thousands of years old, you imply that western history really is as coherent as fascists make it look like; that European or White identity really is an old thing.
It's not as if fascism arose from the aether.
I'll give you a few centuries, 5 or 6 if I'm generous, but not a millennium, much less "many thousand years".
Also while I wouldn't call your average member of the athenian polis "white" supremacist, they were absolutely supremacists.
Which is a very different narrative.