A fascinating book to read if you can find it is Farley Mowat’s book Sea of Slaughter. It mainly deals with the destruction of the wildlife in and around the Gulf of St. Lawrence when the white man arrived, based on old journals etc. However, he does spend a bit of time discussing other areas of North America. Early explorers reported schools of cod so thick you could almost walk on them. Old timers can remember cod that were 5 to 6 feet long less than a century ago. Bird rocks thick with nests - until sailors collecting eggs let the cats or rats get ashore. Passenger pigeons and similar flocks that darkened the sky - hunting consisted of pointing a shotgun upward and collected all the birds that fell after each shot; except the curlews often exploded with a splat hitting the ground, they were so fat for the flight south.
You have to be careful about making generalizations about pre-European Contact North America as there is considerable evidence that before European diseases got loose in Central America and traveled to the north, considerably before Jamestown and the like were settled, the population was much more dense with a lot more agriculture going on. What the Europeans found when landing in places like Virginia was a post-apocalyptic die-off landscape returning to the wild in many places, not a pristine landscape.
That said, there were some regions, like the Pacific Northwest, where food was so abundant that hunter-gatherers could have settled villages.
“several thousand years” is a bit of a stretch. GT was occupied from ~9500 BCE to 8000 BCE, contemporaneous with emmer, einkorn, legume and fig cultivation dates. GT itself wasn’t a cultivation site AFAWK, but it wasn’t so far in advance of any cultivation in the region, as is often claimed.
There’s a paper out that argues that those settled villages were occupied by agriculturalists, but it was a form of agriculture not recognized by anthropologists/Westerners. Unfortunately, I’ve lost the link to the paper or I’d give a cite.
But it should also be noted that hunter-gatherer/farmer is not an either-or situation. There’s a transition period usually lasting for long time (possibly thousands of years) where some food is generated by farming and some by hunting and gathering. The PNW people were likely in that transition.
I’ve similarly seen suggestions that the massive herds of bison on the plains, and the flocks of birds like passenger pigeons “darkening the skies” were not normal, but population bulges a result of the serious ecological disturbances by the arrival of Europeans.
OTOH, the die-off and decline of the mound builder civilization in the Mississippi is said to hav happened a century or so before the arrival of Europeans, possibly due to climate change issues. Whereas the French who settled Quebec, while they did notice occasional epidemics in local natives, never mentioned anything approaching the decimation of the local population.
I’ve noted this in previous threads - I recall a book review of a study of the smallpox epidemic in the PNW native populations. The result was - the biggest problem was the speed at which it spread. Entire villages became sick almost simultaneously and were mostly wiped out. But, where there was one or more immune (previously exposed) people, such as a missionary or someone who’d spent time in European settlements, the survival rate was much better. The mortality rate was the same as for Europeans - about 5%. The problem was most died of dehydration, exposure, or starvation while they were too sick to manage and nobody was there to nurse them.
But the point was that the terrain was such that smallpox did not impact the area until the late 1800’s when places like Vancouver and Victoria were becoming settled.
Also note the lifestyle of the Iroquois - they would burn to create fields and farm and hunt an area, then move on after a few years so a somewhat mixed lifestyle. I presume one of the major impediments to population expansion was lack of metal tools to attack the forest.
I’m not sure how easy it would be to clear a palm tree forest in the fertile crescent. Perhaps river banks and flood plains gave the first non-forest areast open to agriculture.
Not a lot of palm forests there at the time. More oak, with lots of other nut trees - pistachio, almond, chestnut are all native to the region. But there were plenty of steppe and scrubland areas as well. That’s the characteristic set of Mediterranean biomes. Grading into more mixed woodlands in the uplands of Anatolia, Iraq and Iran
My understanding is that there was a sort of informal agriculture consisting of encouraging populations of desirable plants and discouraging their competitors. Not quite up to the standard of horticulture but comparable to how Scandinavians learned to “manage” semi-wild herds of reindeer in a rough symbiosis.