It's been incredibly cyclical, actually. The initial policy of assimilation into white culture through education/Christianity by some Europeans in the very early years of colonization was very quickly followed by a practice of removal/extinction, which lasted for hundreds of years up until the post-1890 era. In the years following 1890 (which could actually be argued to be 1887, which was the year that U.S. Congress passed the Dawes Act, promoting the "Americanization" of natives an actual goal), in which the last Native Americans of the west were subdued and placed on reservations/killed, the U.S. began to earnestly try to force white culture upon natives. The best example of this is Carlisle Indian Industrial School in Pennsylvania, which took in thousands of government-prodded natives to teach them the ways of the white man. Carlisle lasted until ~1920, but the school is most famous for being an athletic powerhouse for a few years before it folded.

However, if the period you're referring to is from Euro contact to ~1830, then the subject gets even more muddled. Even at the point of removal for the Cherokees in the 1820s and '30s, for instance, Christian missionaries (acculturation tactics) had made significant strides in two ways. First, they had accomplished a goal of making Christianity a part of Cherokee life. Second, due to the Christianity (among other factors), many Cherokees were intermarrying white women, which helped speed up the process of culture assimilation.

In short, the U.S., whether through Congress, bureaucrats, or private missionaries/schools, never "moved away" from its assimilation process, yet removal of Native Americans from lands only really occurred when the land they were on was deemed necessary for whites to have control of it (which was typically due to gold found, it was needed for a railroad, or it being "prime" agricultural property).