Keep in mind that any speculative history of an early advanced civilization equivalent in scope to the early Indus Valley civilizations arising in the Mississippi basin 2,000-3,000 BC is so far from the realm of actual developments (and identification with known historical groups) that you have a lot of latitude to imagine all sorts of things, regardless of whether it was a "vanished civilization" or one that continued to evolve and develop to influence later civilizations developing elsewhere in north and central america.
Some logical necessities:
(1) Since maize, beans, and squash were much later imports from mesoamerica, the civilization has to be based on an early development and intensification of eastern woodland cultigens (amaranth, sunflower, etc) and most importantly you need to explain why this intensification was necessary...create some climate change or something that made it necessary. There are also issues about whether the eastern agricultural complex could have supported OTL's Mississippian flourescence in the first millenia AD, not to mention a much more advanced civilization 3000 years earlier, so this is the toughest hurdle to get past.
(2) To be considered a truly advanced civilization, you need some form of writing to evolve. How and why do they do this? calendrical needs? almanacs? trade records? tribute and conquest records? What sort of system is it?
(3) What will prompt the evolution of a true state-level society (one with kings, bureaucrats, military orders, etc) from a simple farming and hunting subsistence? Why do the people submit to authority? Constrained environments?
(4) Domestic animals. Not really essential, but cool to think about. Are there animals that might be domesticated for food or as beast of burden. Explore the feasibility of semi-domestic deer herding, bison herding, etc. Maybe domesticated beaver, black bear, who knows?
(5) If the civilization vanishes, why? and why didn't it influence later developments anyway?
(6) If you have it survive and continue to evolve, you can basically rewrite the entire prehistory and history of north and central america from 2000 BC on. No need to work any contemporary or historical groups from our timeline (Aztecs, Olmecs, Pueblo, Natchez, Iroquois, Anasazi, whatever) into the narrative, since they will have been butterflied away or significantly altered by all the massive changes emanating from the great civilization that developed in the Mississippi Valley. Fun stuff.
But by now, your are really writing a historical fantasy as much as an alternate history.