I was just thinking about how I had seen plenty of images and statues of dogs in pre-Columbian art, but I can't recall ever seeing a cat. Were cats domesticated in the Old World by the time humans had begun to migrate to the Americas? Would these migratory bands have even been able to keep cats, given that they don't travel well? If cats didn't arrive until after European contact, do we know anything about what indigenous people first made of them?
Domesticated cats (Felis catus) aren't native to the Americas, so they weren't around there until the Columbian exchange.
This doesn't mean that people didn't have pet cats from time to time. At the Elizabeth site in Illinois, there's a Havana Hopewell burial mound dated to 25–79 CE. One of the notable features of this burial is the presence of a young bobcat (7 months old or less). The skeleton shows no signs of trauma or being butchered or skinned. But it was decorated with a necklace made from shell beads and faux canine teeth carved from bone. The bobcat was originally misidentified as a dog because its burial resembles more common dog burials (incidentally, it also raises the question of whether some of those other dog burials may have been misidentified as well). It seems likely this bobcat was being tamed but unfortunately didn't survive to adulthood.
You can read about this bobcat in more detail in this paper, if you can get through the paywall.