Pottery intended for use in cooking existed in Libya about 10,000 years ago and may have in turn been derived from Sudan/Nubia. This predates the appearance of pottery in the Fertile Crescent which developed agriculture before it developed pottery in the pre-pottery Neolithic era.
In contrast, pottery was developed before farming in East Asia and appears to have migrated to the West across Siberia in the Mesolithic era. This was the source of pottery technology for almost all of Eurasia.
Indeed, in Russian archaeology, the customary periodization marks the beginning of the Neolithic era with the invention of pottery and not as is the case in Western archaeology, with the beginning of food production, during what Westerners would generally call the Mesolithic era. By Russian reckoning, the Neolithic begins in Russia and only later reaches the Fertile Crescent.
The evidence tends to show that the Fertile Crescent adopted pottery technology from hunter-gatherer-fisherman people in the North (probably ultimately traceable back to East Asia), but a contribution to Fertile Crescent pottery technology from Africa can't be ruled out.