Hi, Charley. "Firing a pot" sounds high-tech, but others have pointed out that people probably made pottery accidentally by building a fire on clay soil. One day they were taking the stegosaurus ribs off the grill, and the ground below had turned to a useful-looking hard substance.
First they pried up the hard layers and used them as paleolithic fribees. 20,000 years later, somebody thought of making the first container. Easy peasy.