Not all land was stolen. Much of it was bartered and sold. Tribes also vied for the pelt trade and would drive competing tribes out. The land we took from Mexico was only Spanish and Mexican on paper. Either one had as much control over the Apache/Comanche territory as Russia had over Alaska. Also the Apaches were driven out and nearly exterminated by the Comanche who remembered that they were nearly exterminated by the Apache when they got some stray horses and learned to ride them a century or so prior. The Mexican govt, wanting a buffer against Comanches, invited colonists from eastern states to colonize Texas in order prevent the raiding the Comanches were doing.

That is most of the territory was not under any tribe’s permanent control, nor was land in the west under control of Spain or Mexico before the Americans colonized it. Also lots of tribes were sworn enemies with each other and more than happy to collaborate with Europeans to drive out their enemy tribes with fewer losses to themselves.