This is going to sound a bit weird, so please bear with me. I was reading up on Irish stew and noted the idea that cauldrons as a cooking technology weren't introduced to Europe until relatively late.
So this makes me curious about pre-European contact Native Americans. I know metalwork was limited on the continent so metal cauldrons per se probably wouldn't have existed, but I also know they made stone bowls and whatnot - did Native Americans have a tradition of cauldron-style cookery? Or was this a less obvious part of the Columbian exchange?
So, are you asking whether Natives made soups and stews, or whether natives used metal cookware for them specifically?
The first answer is quite easy to answer. In both the Triple Alliance and Inca Empire, soups and stews were cooked, seemingly in earthenware or pottery. The Triple Alliance examples come to us via Spanish accounts in the Codices. The Florentine Codex mentions Pozole specifically, which has now evolved to become a national dish in Mexico. The Inca diet was more varied due to the vast geographical area they covered, and was largely vegetarian due to the limited availability of meat livestock. However, Last of the Incas by Kim McQuarrie makes mention of Inca fish stews being eaten on the coast.
It also stands to reason, as a soup or stew is the simplest food one can prepare. Boiling water maintains a consistent temperature during cooking, and so alleviates variation in temperature methods like baking, roasting or frying would contend with on primitive fires.