Get outside and work the land. Provide crops to those who have never been in the countryside. Consider the logistics and the Civil works required for such population densities.
Consider the amount of acreage required to sustain such population densities.
Hundreds of millions in a nation hasn’t been feasible until after the industrial revolution and mass production and delivery of goods and basics which were developed in the US in the 1900s.
Discern between missions, settlement, colonization, and immigration. Entirely different motivations and systems of governance for each.
Most of what you are studying is historical revisionism.
Politicians attempting to mislead the younger generation to think in terms of their present local culture, instead of actually studying the mechanics of past human endeavor.
In regards to engineering, about the only engineering aspect not found in Europe during the time of the Conquistadors, was the catenary and suspension bridges discovered with the Incas in South America.
There is only so much which can be done with gravity flowing irrigation and cesspools, oxen and paddled/sailing boats and barges, unimproved trails and thatched or adobe huts.
In regards to engineering wonders, I suspect more recent studies regarding the Nephilim and Giants actually touch on unexplained sources in the Americas, though the same or similar structures are also found in nearly all ancient history throughout the planet...but I digress.
I understand lots of history taught in the last 30 years assumes millions of people lived in those past civilizations. Only problem is the numbers don’t add up, when actually trying to implement such empires, before the internal combustion engine or steam powered systems.
Discern between missions, pioneering, settlement, colonization, and immigration. Entirely different motivations and systems of governance for each.
BTW, your self assessment indicates you are more Latino than Hispanic.
Very good points. That said, the Chinese kept quite good records (for the time). Their population was approx. 123 million in 1200, dropped to around 60 million at the beginning of the Ming Dynasty (Mongols, famine, and diseases), and the Chinese population by the end of the Ming Dynasty was near 150 million. Of course, while not having steam power, the Chinese were quite advanced on a national scale in many of the other things necessary to sustain a fairly large population. But even they could not maintain a population over 100 million for long periods, when famine and disease struck, until some further advancements were made...
The best estimates for the pre-Columbian North American population vary wildly, from 2 million to a maximum of 18 million.