Like its neighbor Burma, Thailand was more influenced by India than by China. People in Thailand were probably becoming Buddhists by the 200s BC, in the time of the Mauryan Empire in India. On the Silk Road, Thailand sold spices and beeswax.
Kingdom of Funan
Starting in the late 500s AD, the Kingdom of Funan got started. The kingdom of Funan collapsed in the early 800s AD.
In the 1200s, the Mongols came south from China and conquered the Khmer Empire of Thailand as well as Burma. The Mongol conquest reoriented Thai culture more towards China. A Chinese ambassador, Zhou Daguan, came to Thailand and wrote a book about what Thailand and Cambodia were like.