So there WAS vast expanses available by that time, even without intentional genocide (which also happened).
A large percentage of the land battles of the War of 1812 were fought between the US and natives because the US wanted the land of the natives to become open space so the natives allied themselves with Britain.
Lewis and Clark would not have survived or even made it to the coast if they had not had help from most of the tribes they met along the way. Of course we displaced all of the natives they met eventually.
I just read https://en.wikipedia.org/wiki/Lies_My_Teacher_Told_Me so that may bias my opinion.
2. There is still a huge amount of open space in America. In 1800, there were only 5 million citizens, compared to 323 million today.
3. Natives lived all over the continent. Europeans landed where the ocean ended.