The fact that a religions occur in every culture, and there is enormous variety as to detail, fits with the idea that religion is an epi-phenomenon, or a purely cultural one. It is probable that Neanderthals had religious feelings, because they seem to have buried their dead with some ceremony. It might be recent, if it developed independently in humans and Neanderthals, or it might go back a long time, to the common ancestor of both, half a million years ago. In either case there could be some predisposition in the genetic makeup of our ancestors that led to religion. It is not always reliable to reason from present roles of any trait to past reasons or mechanisms of origin of the trait. However, if we want to think about the hypothesis of a genetic predisposition for a trait, one standard procedure is to look for the trait, or glimmerings of it, in other organisms. Considering religion as a trait, we can only go by the behavior of animals. They are not capable of conversing with us. What comes to mind is the report of elephants taking a preferential interest in the bones of elephants over those of other animals. Jane Goodal reported high levels of excitement in chimpanzees in response to heavy storms and waterfalls (here is an interesting link). To some extent, the distinction between culture and other human traits is fuzzy, since it is likely that culture influenced genetic selection in hominins from very early times, simultaneously improving the anatomy required for tool making, and improving the tools themselves. It seems to me at least plausible that religious feelings or behaviors stem from or need a threshold level of consciousness. There is at least a hint that elephants and chimps have evolved to that point.