The historical record is murky admittedly. Many primary sources we rely on for this region are biased and fantastical retellings of history from centuries later. That being said, migration patterns and linguistic groups are often used to paint the picture of state formation. However, that too has its limitations on time periods and is especially limited in how certain states and nations were formed

"Proto-states": Those caveats aside, the indigenous/pre-historic peoples in the two countries are typically accepted to be the Pyu, Mon, Wa among others. The Pyu inhabited Upper Myanmar in the Irrawaddy valley, the Mon in the coast of Lower Myanmar and Lower Thailand and the Wa in the Shan Plateau and Northern Thailand. We have archaeological records inidicating that the Pyu had city states exerting influence outwards and that the Mon formed loosely connected polities. Both are version of "mandala states"- polities that focus more on the development of their capital city as a form of exerting influence and power rather than on securing borders. This philosophy was informed in part by Buddhist-Hindu ideals. Chinese trade accounts say that the Pyu were so peaceful that they refused silk as it harmed silkworms. We have few records of conflict, but we do see the Mon in Lower Thailand "Lavo" send people to settle, "tame" and convert Northern Thailand "Haripunchai". It's again unclear.

Burma: In the late 9th century, the Kingdom of Nanzhao in Yunnan raided the Pyu city states. Sometime around 846 CE, the Mranma horse-raider people settled the depopulated regions near modern day Bagan, Myanmar. Nanzhao supported the Mranma who helped them raid as a way to suppress Pyu dominance as they expanded their kingdom into Northern Myanmar. From there, we have about 200 years before the newly established Bagan city state conquered the other Pyu city states to form the first Burmese kingdom- Bagan. Granaries and agricultural innovations allowed Bagan to reap the rewards of Nanzhao's conquests and grow in population. In those 200 years the Mranma gradually intermixed with neighbouring Pyu states and slowly converted to Ari Buddhism and adopted many Pyu cultural ideas becoming Burmese. We have good accounts of the conquest post-1000s but not much as to the what spurred it. Even this kingdom was not a hard-bound polity, still having many of the Mandala State ideals. But there was much more state-making and focus on militarily keeping other cities within the kingdom.

Thailand: The Bagan Kingdom would rise and fall to the Mongols before the Tai ever got to Thailand. The Tai people had been pushed south by the Mongols and came to found settlements in Ngoenyang, Northern Thailand. I'm more of a historian on Burma so I can't speak to as much detail, but the Tai eventually formed a tripartite rivalry in Northern Thailand with Sukhothai, Lanna and Lampang. Lampang was a remnant of the Mon kingdom Haripunchai after being attacked by the Khmer Empire. Sukhothai was pushed southwards and became a protectorate of the Mon kingdom of Lavo. Lavo, itself, became a more centralized (but still not centralized) state due to the influence of the Khmer. Thailand had been much more "Khmerized" evident in Thai culture and language up to the modern day. Lavo itself waned in power and in the 13th century, Sukhothai rebelled against Lavo. Their success started the decline of the Mon in Thailand. In the 1350s, Lavo and a local Thai ruler cofounded Ayutthaya near modern-day Bangkok and laid the foundations for a heavily fortified capital from which a Thai kingdom uniting the Chao Phraya valley came forth.

Zomia Another part to remember is that much of "Thailand" and "Myanmar" were never part of the centralized state. Some parts of Myanmar aren't part of the centralized state to this day. This is academically been termed as "Zomia"- the anarchic highland borders that the lowland kingdoms largely could not control. A good portion of these people are indigenous/pre-historic. One important except is the Tai Yai or Shan people. While Sukhothai eventually lead to the formation of Thailand, Lanna and the remaining Tai city-states pushed northerwards into Wa territorities forming settlements and city-states. The city-states formed a loose coalition around the 16th century but remained largely mandala-style independent city states swearing fealty to Burmese, Thai and/or Chinese kingdoms until the onset of colonialism and the formalization of borders and nation-states.