Pre-columbian domestic dogs of the Americas trace their ancestry back to Eurasian wolves rather than American wolves, so they are descended from the same domestication event as all other dogs. The oldest dog remains in the Americas are about 10,000 years old, just at the end of the Paleoindian period and the transition into the Archaic period. So some Paleoindians had dogs, but at the moment its not clear if all Paleoindians did or if dogs came over late during the Paleoindian migrations.

Here's some suggestions for further reading:

Tito, Raul Y., et al. "Brief communication: DNA from early Holocene American dog." American journal of physical anthropology 145.4 (2011): 653-657.

van Asch, Barbara, et al. "Pre-Columbian origins of Native American dog breeds, with only limited replacement by European dogs, confirmed by mtDNA analysis." Proceedings of the Royal Society of London B: Biological Sciences 280.1766 (2013): 20131142.