The pack behavior still extant today in people and in many other mammals can only have been stronger when our parents were more centered in the physical, and that centering really prevents a lot of lingering in illusion. This meant, and this is not the speculative part, there was a vigorous nonverbal link between the people. My guess is that this included a stronger psychic component than is extant today among men who are ruled by the verbal.
Regardless, the origin of the idea of a god may have come from an individual, part of something larger, the rest of the pack, his family and farther relations-- the origin of god may have lain in the awareness of this extensiveness beyond oneself, a larger something than oneself which was perceived, and which was recognized as being a protection and aid that was more than one, by oneself, could have supplied or guaranteed.
Perhaps this awareness came about like this: These early folk hunted in packs too, but surely, there were times, times of hardship of a variety of sources, or, perhaps when one was some kind of outlier, some times, when a person had to hunt by himself. Then it may have come to this individual that he needed and depended upon, something greater than he himself was.
That he gave, and many times, across the planet, men did this again, a name of what we call a deity to this, is not surprising. Whenever a verbal ability grew, what Jan Cox said, was a "falling upstairs," it would be convenient to mention something stronger than oneself, something which worked for one's benefit. Whether or not this calling of a tribe, by a word which we call some deity, is the whole story of the origin of god, this story is not meant to preclude the later reality of what people said about their deities. My account of a individual in a larger tribe, appreciating this sense of being part of something larger, need not be the whole story, to be of interest.