"Ancient" is kind of a relative term. If you're talking about Asia or Europe, ancient refers back thousands of years. In relation to the Americas, however, it describes a time that in the rest of the world is known as the Renaissance or the Early Modern Period. That's not because North and South America don't have history going back further, but because that history is largely unknown.
The oldest American civilizations, the "great" civilizations, are mostly found in Mexico and South America: the Aztecs and Maya in Mexico, and the Inca Empire in Peru. They all left behind plenty of artifacts, but written language was scarce, and the hieroglyphs archaeologists have found are largely difficult to translate. We have mostly religioius sites, ruined private and civic buildings, and artwork to piece together their stories.
It also doesn't help that the first Europeans to meet up with these groups were fierce and greedy. Explorers and traders were more interested in gold and slaves than they were in anthropological study, and they spread chaos, fear and violence throughout an area no less violent but maintaining a sense of balance before the European arrival.
In North America, Indian tribes were smaller and less advanced culturally (art, architecture, math, etc.), though alliances like the Iroquois League evidenced a highly advanced social organization and government. The League was an association of various tribes protected by alliance, and it was already firmly in place when European settlers and explorers first arrived in the 17th century.
20th century historians like to posit theories of the origins of all these cultures, and also to villify the "white men" as much as possible. Some of the former are pretty far-fetched, and most of the latter attempts are immoderate. Yes, men like Cortes were unscrupulous and did much more harm than good, but there were good and bad explorers, and the natives weren't exactly saints, either.
The best thing to come of the European discovery of the New World was the spread of the Gospel to people who'd never heard it. This is ultimately the best part of any story—the part where humans, bloody and wicked and on the brink of collapse, are redeemed and renewed through the working of the Holy Spirit. Some of the most compelling missionary stories came from the wreckage of ancient American cultures, and for that we can rejoice and thank God for His mercy and lovingkindness, even to the most oppressed people.