Only recently have we been able to overcome it.
Were the seeds of religion sown in primitive peoples observations of and attempts to reckon with all the scary shit they would witness in the natural world? Absolutely. But any "definitive" statements on pre-historical belief systems are probably anthropological hearsay, possibly weighted by our current knowledge of and feelings towards religion. What was going on back then could have been just slightly more complex than a dog hiding under the bed when there's thunder.
And keep in mind, we're talking about a 200,000 year run up to recorded history. However, I'm sure there was a more complex oral tradition of storytelling and mythmaking that was starting to develop before the Sumerians took off.
Weherein we have some evidence that such was not the case with moving towards public law.