Dude, America is basically 52 nations in one. All of it was conquered and stolen/annexed. America is by far the most successful conquering/war-mongering nation in the entire history of this planet.
Most of America's land was purchased, not conquered, especially in the 17th and 18th centuries. America (by which I mean the preceding French, Dutch and English) did not need to conquer that much land from Natives early in its history in order to build a presence there, because 90% of the Native population died of disease before the settlers showed up. The civilization we think of as America in Civ descends from the settlers who moved in (often expanding ahead of their governments or militaries), not the colonial traders from Europe who preceded them, declared the national rights and spread the diseases.
Stuff like the forced marches, mass relocations, and purges didn't happen quite so much until after America had asserted its territorial dominance in an area, with formal diplomatic recognition from other countries already secure, especially east of the Mississippi.
It's not like atrocities didn't happen, but it depends on whether you see the massacre of Natives as America committing crimes against its own people, whom it should have been protecting and looking out for because it already controlled their territory from previous deals and conflicts, or against foreign peoples who controlled land that they wanted and were only now seizing.
How sovereign, really, have sovereign Native nations been in America? This is particularly interesting when compared to other overland empires like Russia or the Holy Roman Empire, all of which have different timings for when and how they expanded versus when and how they exerted authority over multinational inhabitants.
And then the question is how do you regard the legitimacy of deals that America made with other colonizers over territory they had claimed to own by rights - like the Louisiana Purchase and the Florida Purchase Treaty - or, how much, at the time that America took ownership of land by these means, it was still "owned" by the natives that Spain claimed were under their empire, and was only really incorporated into "America" later, in the conflicts between the government and the nominally sovereign Native groups.
And of course there's the Mexican War as the big exception and clear-cut conquest.
I don't think an American Civ that goes by a "settle/purchase/defend" strategy or uses force to back up trade deals and city state influence rather than going for outright full-on conquest is out of character for how America actually expanded its territory. But I don't think an America that gets on a bunch of horses and goes out and takes over another country for keeps, fully assimilating it, feels like America rather than other Civs that are much more well-known for that.
