That seems quite plausible to me. At least part of our beliefs in gods could well be the result of our interactions with our parents. If so, that part would be psychological rather than genetic in origin (that is, mostly the result of nurture, not nature). Universal human traits are commonly assumed to be genetic, which makes sense; but the universality of this particular trait could just follow from the universal way in which children are totally dependent on their parents (or equivalent adult parental figures)—no genetic predisposition needed.
Here I wrote something very much aligned with your ideas: “…with respect to the ‘Big Gods’, perhaps there’s some validity in considering a purely psychological angle. For example, one could conjecture that the security, comfort and unconditional love that most humans enjoy in their early childhood, coupled with the perception of our parents’ being all knowing and powerful and with their constant application of rewards and punishments, might be enough to make an adult feel a painful and disconcerting void were all this not replaced with something equivalent.”
By the way, I recommend the article to which I replied with those lines. It’s very good and precisely on this topic.