The lateen sail was paired with the square (”Roman”) sail during the Middle Ages, making it possible to do both — take maximum advantage of tailwinds, and tack “into” the wind (which always goes slower). It was in use in the Indian Ocean, and made it’s way into the Med via the Muzzies — but it’s difficult to believe that it had no prior existence. It was probably in use not long after the first discerned use of watercraft on open seas (which is 800,000 years ago). AFAIK, ancient sails have never been found on the seafloor, neither has any other significant amount of ropes, riggings, or fabrics, that would be a GREAT find, maybe a vessel preserved as were the Pisa boats.