Yes, you can. Foreigners can own a house in Thailand. How else there are thousands of foreigners (“farangs” in Thai) living in Thailand? And not all of them live in a condo… Some would own a small affordable, cheap house somewhere in East Pattaya, Central Pattaya, or perhaps even in Bang Saray. Or a “prestige” villa property with a private pool close to the beach in Jomtien or Pratumnak...