I think of neolithic clay figurines of animals and people as basically portable cave paintings and they are probably the way fired ceramics were discovered. In a hunter-gatherer type of setting, it seems natural that legends of past hunting successes, plans for tomorrow’s hunt, and tales of how prey animals behave and how a brave hunter can prevail, might be discussed - perhaps roleplayed using little models of animals and hunters made from mud - even unfired clay - basically just dry mud - is surprisingly durable for such a purpose when the models being made are small enough to fit in hand.
If such discussions took place around a fire, it’s inevitable that eventually, one of those little figures will end up in the embers somehow - and the next day, someone notices that the little mud animals are now as hard as stone…
I experimented with this a little bit during a different craft project related to wild clay recently - starting from a rolled ball of clay, the primitive form of an animal can be shaped by just pinching it a dozen times or so to pull out the legs, neck, head, tail, etc. It dries in less than a day, and even in an ordinary wood fire, it fires to earthenware ceramic in about half an hour - this is my experimental animal figure after firing in the embers :