Of course it is possible that the tradition goes back more than a thousand years from when it was first attested, but we have no material evidence of that whatsoever. No statues of a goddess surrounded by eggs and rabbits, no amulets of protection, no recorded myths, no references to something similar from Greek or Roman sources, nothing. This is in contrast to beer where we have actually found remains of beer from long, long ago.

It certainly existed for generations prior to when it was first written about .. as much of all human activity did.

We have actual remains of rabbits from long long ago.

The point being much human activity leaves little trace, we'd be wise to not assume the only human activity was activity that left a pyramid or giant stautue in its wake.