So literally just teaching early humans how to cultivate the molds that can kill bacteria would change the trajectory of human history.
Shit just teaching them the concepts behind science and (present day) basic stuff ("no the volcano is not erupting because the gods are angry") could probably head off religion entirely.....SOMEBODY GET ME A DAMN TIME MACHINE
I suppose it's a matter of what the primary early driver of religion is. I think early on, that was moreso a way to explain the unknown and help quell fear and then came the purpose filling.
I think you may be right that it would develop no matter what, but if it truly does develop as a method primarily for purpose filing rather than as a method of control and fear soothing then maybe it wouldn't have been so entrenched the way it is. This "Religion first" mindset and then later on "religion first, science second". A simple change like "Science first, spirituality/religion second" would likely changed a LOT of things for the better in history.