The Iroquois had farms, you know. They grew corn and lived in a communal system where unused land was shared, but there was enough for everyone to have their own area as they wanted. Women had important roles in the labour force and political system. Famine was apparently quite rare, to the degree that the first Europeans across the pond were envious of their food security.
Down south, the Aztec capital was built in the middle of a lake, and had probably around as many people living in it as London, Paris, Venice, and Lisbon combined. The marketplace alone was around the size of a European capital. Tenochtitlan had aqueducts made out of terracotta, and the people bathed twice a day and drank spring water from a separate source. The palace had multiple zoos, gardens, and aquaria, and the nicer parts of the city were built entirely out of brick and masonry. The big temple in the middle was hundreds of feet tall, and only a couple meters shorter than Notre Dame in Paris.
Of course, all of that was destroyed, completely and utterly.
The myth of the romantic Age of Sail explorer is not compatible with the power structures of the time. What king would send perfectly good ships away "just to see what was on the other side", when there were political rivals to outcompete and usurp on this side? And what king would survive sending such resources away, if they did not gain a profit from doing so (through whatever tactics of exploitation were most expedient)?
Certainly the world would have been quite different if Columbus and Cortés decided to work on themselves, instead of concluding that the Earth is shaped like a tiny pear so they should raze a couple cities they just found out about, or whatever else was going on in those men's heads…