Animal domestication
There are ways of doing this, but they have their drawbacks.
1) Have a subset of the North American ice age animals that went extinct survive. I did a scenario years ago where one of the North American llama species survived in a remote corner of North America. Most likely candidates for survival: North American species of llamas and peccaries, North or South American horses, Mammoths, and some of the big (up to several hundred pounds) South American grazing rodents. There is no guarantee that any of those could be domesticated. Zebras apparently can't be, so North American horses might not be easily domesticated. North American llamas might not be either. Mammoths would be unlikely domesticates. The Indians would probably have to domesticate something less formidable first and learn the tricks of handling domestic animals before they tackled something that formidable. The North American peccaries might have a shot if they were less fierce than the South and Central American species that survived.
The problem with scenarios like that is that the divergence would have to be at least 8 to 10 thousand years ago. No Indian individual and probably few Indian tribes of our world would ever have existed with even a minor change that far back. I sort of tried to finesse that issue by having my surviving llamas survive in a little pocket up in the mountains, protected by a disease that killed off human hunters who tried to encroach. Even with that, butterflies would change a lot of things in a hurry.
2) Have the animals that the Indians domesticated historically spread further. Llamas, alpacas, and guinea pigs in the Andes made a decent group of domesticated animals, especially the llamas and alpacas. The problem was that they were adapted to the cool mountains, and didn't do well in the tropical lowlands to the north, east, and west of the Andes. If some lowland Peruvian group had managed to breed llamas that could withstand the heat and humidity of the coast early enough I could see llamas spreading along the sea routes that connected coastal Ecuador to the coasts of Western Mexico, and from there to the nomadic tribes of northern Mexico, making it easier for the Chichemecs to adapt to horses and probably giving the Spanish an even harder time than they had historically. Metallurgy apparently spread by that route. Llamas could have too. Of course depending on the timing of all this, you still might not have a lot of the historic Indian groups or individuals.
3) Have domestic animals from elsewhere arrive earlier and/or spread faster. There is some (controversial) evidence that chickens spread from Polynesia to the coast of Chile in late pre-Columbian times. They hadn't spread through most of the continent though. Get them there a little earlier and add the pigs that the Polynesians spread to most of the islands they colonized, and you could end up with some interesting changes. There is some (again controversial) evidence that Polynesians may have been in sporadic contact with the ancestors of the Chumash Indians in southern California. Get domestic chickens and pigs spreading from there too and you might have something interesting. For that matter, you could have a major early Spanish settlement voyage get pushed into the North or South American coasts by a storm and establish early populations of cattle, horses, and pigs, giving the local Indians an extra fifty to a hundred years to adapt to them. If horses started spreading in North America in the very early 1500s, for example, that would make for a very different Indian culture facing white settlement. Again, you've got to be careful with this, because in all likelihood at least some of the major Great Plains tribes would either not exist in this scenario or not be plains Indians.
