I think it's very likely there were ancient giants that thrived in a time in our distant past where earth's conditions were favourable for optimal genetic expression, as was the case with dinosaurs, etc. There's very good evidence for this.
These giants would have dominated and ruled like gods and would have had their own mythology where they claimed to have descended from gods, such as we read of in the book of Genesis with the Nephalim.
I think if you are looking for a non-supernatural explanation for the origins of religion, the existence of such ancient 'god-like' giants and the mythology they passed on is probably the best explanation.
Fascinating series to watch here:
http://www.youtube.com/watch?feature=endscreen&NR=1&v=ppMQIdQLETI