The United States made two main acquisitions of land after 1812. First, it took much of what is now the Southwestern United States from Mexico in the war with that country in the 1840s. Second, at roughly the same time, the US got what was called the “Oregon Territory” in a treaty with the United Kingdom. The US and the UK had been jointly occupying the region and they divided it up in 1846.
The impact on the Native Americans was not immediate, but it was profound. When the US took all of this land, it meant that the Americans would, eventually, want to settle all of it. That meant that there would no longer be any place for the Indians to live in their traditional ways. When the US acquired all of the Lower 48 that it now holds, it meant that the Indians would inevitably end up fighting the Americans for control of the land. Since the Indians were relatively few in number and were not technologically advanced, they were doomed.
In this way, the acquisition of territory after 1812 meant that the Indian nations were doomed to be destroyed or pushed onto small reservations in marginal areas of the United States.