It's almost inevitable to discover once we started using fire to cook. The fat would drip into the ashes of the fires. Over time, and with a bit of rain they would have discovered some pretty crude soap. I wouldn't be at all surprised to find that hunter-gatherer societies routinely gathered the soap from the previous year they had been there in any given area.
They probably thought it was magic, because why the heck would fat and ashes cause that, but it's a neat little double soluble molecule.
They didn't either. Bathing regularly seems to be a fairly modern concept for us, but we have found evidence that they used it to wash food containers, furs, and clothing.