Were there any religious or cultural assumptions about it being the edge of the world? Was there any speculation about there being other continents and civilizations? Mostly thinking of North America but if Central and South Americans had any ideas then I'd be interested to hear those too.
The desert people of the American Southwest generally understood the concept of oceans as not being fundamentally different from a large lake or stream. Among the [recorded] creation myths of the O'odham peoples, at least two contain gods or demigods turning small rivers into vast oceans, splitting apart the original peoples of the Earth, although the survival of remote peoples is left ambiguous. One of these stories later goes on to discuss the people who survived the flood on the other side of the ocean, who were conveniently white-skinned. Another passage from the same source states that another group of people over the ocean were in fact dark brown. Both of these groups were the result of mistakes in creation, after which the perfectly colored Hohokam groups were created. As prophetic as these may sound, our one source of these tales was recorded from a drunkard by a priest in the 1930s. Given that it is the only semi-complete history of the O'odham remaining today, we have no means to determine how far back the individual elements go.
Among the Hopi and other Puebloan peoples, we have an understanding that the oceans were not the complete end of land. At the very least they understood that people lived in the islands off the Atlantic and Pacific coasts from trade with groups living nearer to the sea.
Both groups had an accurate understanding of the geography of their continent between the oceans and an understanding that humans could live on the water as their neighbors did. It's not impossible that they conceived of other lands similar to their own across the water, which was understood to be similar to a large river or lake. The stories we have hint at this understanding, but the near-complete absence of historical records about the O'odham and Yuman people make that suggestion speculative at best. The situation among the Puebloans is little better. While they clearly understood the concept of sailing quite well, the myths make scarce mention of foreign lands that would not have been visible from shore.
Bahr, Donald M., et al. The short, swift time of gods on earth: The Hohokam chronicles. Univ of California Press, 1994.
Courlander, Harold, ed. The fourth world of the Hopis. UNM Press, 1971.