The earliest record of soap is in Babylonia around 2800 BC. Soap is the product of fat and lye. Lye is a byproduct of wood ash. I can imagine people sitting around a campfire, cooking meat over an open fire. Grease from the meat drips down into the ash. The next morning, when the fire has cooled down, someone picks up a glob of sticky stuff out of the ash and rubs it between their fingers. If gets slippery and produces a little foam.
I read in a book by Bradford Angier, that wood ash is a great way to clean greasy pans when camping. I had to try it. I took a small handful of ash, scrubbed the pan with it and, sure enough, it created a bit of soap. It would be reasonable to think that rinsing the pan would clean the hands too and from that would come bathing and washing clothes.

Do You Have an Ancient Craft?
RagtimelilJun 29, 2012
The northerners were a little slow to catch on to soap. Hence the legend that one of the English queens, to her minions admiration, took a bath "once a month, whether she needs it or no."
JasmineJun 29, 2012