Reddit reviews Olmec: Colossal Masterworks of Ancient Mexico

Anything is possible, I suppose. However, it's unique until proven otherwise. Someone had to be the first, and maybe it was these folks. I had a mentor tell me once that young archaeologists are too stupid to know when they're wrong, and that's why we go out and end up changing paradigms with our research. (Within reason, of course - archaeology is destructive, which is why sites aren't excavated fully anymore. We would destroy all our data if we did.)

Based on what we know now, these people would have been hunter-gatherers (perhaps practicing very early forms of horticulture and pastoralism), who believed in an animistic/totemistic/shamanistic religious tradition. This is what is represented at Gobekli Tepe.

Equally as old in the Incan world isn't possible. The Incan empire started in the 13th century CE. Concerning theories about human population of the Americas, people could have populated the New World as early as 30 ky BP, but the most current theory argues for a population period of c. 11 ky BP (right around when Gobekli Tepe was built).

There are a bunch of publications that, from your comments, I think you might enjoy. Ian Hodder has written a lot about Catalhoyuk (The Leopard's Tale for example), which is another very old site, extremely well researched. The Olmecs would also be of interest to you, they're notable for a lot of cultural features, especially megalithic art.