This is a pretty crazy idea, but one that's been floating around in academia and pop culture since the 1970s:
That until c. the late Bronze Age, humans were generally incapable of complete self-awareness. Instead, one part of the brain ("independent" of a person's core consciousness) signaled information to the rest (constituting a person's core consciousness), and people didn't understand this "voice" as originating from themselves but rather believed it to be an external voice.
It was analogous to modern-day schizophrenia and people thought they were communicating with the divine. This was not due to anatomical differences from modern humans but instead it was a cultural phenomenon. Or, that is, when civilization attained a certain level of sophisticated thought via the development of language and so forth, it altered the way that people perceived their own consciousness.