Yesterday, I revisited the topic of an Ainu/Emishi/Jomon-dominated Japan, and here's what I've found:
(I know it's almost far-fetched, but it's irresistible...)
If they became fishermen it could help them a bit.
They see a Korean boat wash up on the beach, get some ideas from it and start using the maritime resources more efficiently. They get a population boom and form some villages and more structured society based on fish.
When the farmers come over, they won't be so overwhelmed and can either absorb the first few new comers, getting the crops that way, or raid them and get the crops anyways.
The Ainu (Ezo?) would probably end up importing most of the Chinese package, though they might very well keep their native grains (foxtail millet, deccan grass etc) more than OTL Japanese did, thus leading to less reliance on paddy agriculture. So, one difference might be that the idea of a centralised government could be so difficult to enforce, and so expensive to try, that it would, at most, remain an ideal.
OTL Japanese were bad enough pirates to China, and they theoretically revered Chinese civilisation. Our Ainu might even conquering some of China's coasts, or at least be an even worse plague to east Asia. They might look further afield than China, too, and adopt more from India/Indonesia.
Buddhism and Confucianism have been so successful, they'd probably make inroads here, too. But Confucianism's reverence for tradition might end up reinforcing nativism, and Buddhism remain a slandered minority.
One detail...the Chinese have fox demons. If the natives have to fight them long and hard, they might feel the foxes are somehow the national symbol, or even claim some descent.
This is extremely challenging to do, but the best POD would be to butterfly away the arrival in the Japanese islands of the mainland newcomers in the Yayoi period, starting around 300 BC. If this component of the OTL Japanese ethnicity remained on the mainland - in Korea or Manchuria, as much of the archaeological and linguistic evidence indicates - then potentially the Ainu (and whatever other Jomon-period ethnic groups may have existed) could have continued to occupy the Japanese islands and maybe taken the place of Japan in this ATL. There would likely still be heavy influence from Chinese civilization, but the specifics of *Japan would be based on Ainu/Jomon culture rather than OTL Japanese culture. At the same time, Korea and Manchuria would likely be more ethnically/culturally/linguistically diverse in this timeline, potentially including cultural and linguistic forms recognizable as Korean and Japanese, or at least close relatives. So, assuming a pre-Yayoi POD of 300 BC or earlier, we would at least create the conditions necessary for a TL that meets the OP's specifications.
In summary, with a PoD that ranged between 8th and 4th century BCE, with possible later immigration from Korean peninsula, particularly from the south (Yayoi) and the spread of Chinese influence in the later centuries, what would the possible role of an Ainu "Japan" in the regional history of East Asia?This would essentially require a PoD long before the 8th century BC, which might in turn render the alternate East Asia entirely unrecognizable from that of IOTL. Specifically, the chaos from the Spring and Autumn/Warring States Periods may have caused migrants from China to flee to the archipelago, while later developments led to friction between the Yan and Gojoseon, in which Liaoxi was conquered from the latter, triggering migrations southward into the peninsula, pushing many of the inhabitants eastward into Japan.
In order for the widespread chaos to be butterflied away altogether, China would have had to remain stable for a far longer period of time. This may well have been impossible as remote frontier regions began to assert their independence from the Zhou, making it essentially inevitable that neighboring entities would eventually go to war with each other.
Also, Japanese toponyms are only found in areas south of Pyongyang, with none in Manchuria, which has a high density of Korean ones. Genetic research also suggests that the respective populations in the peninsula and the archipelago may not have changed significantly, suggesting that founder populations gradually assimilated local inhabitants.
(I know it's almost far-fetched, but it's irresistible...)