So I've actually been reading a book which touches on this exact topic.

From my understanding there is limited evidence regarding when and where rice was first domesticated. However, the earliest appearance allegedly take place in India about 2000 BC. That being said, there is evidence that suggests it may have first appeared in Thailand even earlier, though I haven't actually looked into this.

There exists a lot of Sansctitic recordings of rice and the many ways it can be prepared and cooked. Despite such, there still doesn't appear to be much information regarding its origin.

Studies of the crop have given us some insight into the enviorment it likely stems from. The rice cultivated in East Asia today is 'Oryza Sativa' and its ancestor is likely 'O. Perennis'. This is a deep-water type of rice which is found throughout South East Asia. If the studies are to be believed then it suggests that rice was first cultivated in the wetlands of South East Asia.

Due to the nature of rice farming, it likely did not spread out from this area and become a domesticated crop until much later. As the technology required to farm it outside of its natural enviorment did not arrive until much later. I dont know the exact date, but rice likely did not reach Japan and Korea until about the seventh century A.D. So that may shed some light as to when it first began to spread outside of its place of origin.

Sources: -The Prehistory of China, an Archeological Exploration. Judith M. Treistman