There's archaeological evidence of a Mayan sweat lodge dating from about 900 BCE, which is the oldest example yet discovered in the Western Hemisphere.

There have also been many archaeological finds of later sweat lodges throughout North America: for example, California, Cahokia, Indiana, and various parts of the Southeast.

Sweating seems to be part of a complex of rituals associated with shamanism, which is diffused throughout the Americas. Whether people built structures specifically for the sweat is another question, however, and the earliest unequivocal example we have is the one unearthed in Belize.