Were the dogs of the Americas domesticated independently of those in Eurasia?

While this is a question about the history of dogs, the answer must be based more on science rather than history, since the Old World domestication of dogs was prehistoric, and if there was an independent American domestication, it was also prehistoric. The solution can be found in genetics: pre-Columbian American domesticated dogs were descended from Asian domesticated dogs. In recent centuries, there has been genetic mixing with European dogs (which also originally descended from Asian domesticated dogs), and in some cases a lot of mixing.

Interestingly, there are (modern) North American wild/feral dogs that are (mostly) descended from pre-Columbian American domesticated dogs, while South American wild/feral dogs are descended from European domesticated dogs.

As for the timing of the domestication of dogs, we have evidence from both genetics and archaeology. By about 14,000 years ago, it appears that dogs were domesticated, judging by the burial of what appear to be domesticated dogs together with humans. Genetics places the divergence between grey wolves (the ancestors of domestic dogs) and domestic dogs about 20,000 to 40,000 years ago. This is complicated by the genetics of wolves which strongly suggests that modern grey wolves descended from a small regional population about 25,000 years, and are less genetically diverse than their ancestors before this genetic bottleneck event. It's possible that this ancestral population lived in the Bering land bridge at that time. Other similar ice age population/genetic bottlenecks are known, perhaps most famously that for cheetahs, dating to about 10,000 years ago (the last ice age). Further complicating things is the possibility of genetic mixing between grey wolves and domesticated dogs after this bottleneck.

But, in any case, the latest reasonable estimates for the divergences of dogs and wolves is about 20,000 years ago, and archaeology suggests domestication before 14,000 years ago. Thus dogs were domesticated, and wideapread across Eurasia, long before the peopling of the Americas (give or take some much earlier estimates, but these don't invalidate the close relationship between American and Asia dogs which could still have come in later migrations of people to the Americas after these controversial very early dates). The domesticated dog went along with people who walked from Siberia to North America across the Bering land bridge during the last ice age. The dog might or might not have been domesticated when the first people crossed the Bering land bridge, but definitely was thousands of years before the land bridge went under water.

There are animals that were domesticated independently in different places, including pigs, cattle, and possibly sheep, as I discussed in https://www.reddit.com/r/AskHistorians/comments/gaa29q/short_answers_to_simple_questions_april_29_2020/fpcmloe/?context=3 - one animal that was domesticated independently in the Old World and the Americas is the duck, with ducks being domesticated in China perhaps 6,000 years ago, and the muscovy duck being domesticated in the Americas perhaps 2,500 to 3,000 years ago.