The number of plant species domesticated by ancient American populations is HUGE and easily outnumbers the count from the Old World.
So, what you had in America were advanced agriculturalists (with, for example, squash, beans, popcorn, strawberries, and myriads of other tasty delights) being overrun by people little removed from their hunter/gather, migratory herdsman traditions.
One of the great hot-houses of agricultural development occurred in Kentucky and Southern Indiana.
The most renowned civilization, that of Sumer (the first one we know of) was started up by migratory herdsmen!
The second most renowned civilization, that of Egypt, was also started up by people who moved in from the dying grasslands of what became known as the Sahara Desert. They may have herded domestic animals, or not ~ most likely they were great hunters from the plains!
The Yayoi brought agriculture to an already civilized and organized Japan. The Jomon were developing agriculture in the far North where conditions were tougher, but otherwise they could depend on hunting and gathering in the rich hardwood forests then covering Central and Southern japan!
Dollars to doughnuts Hunter/Gatherer societies were capable of enslaving farmers and doing with them as they wished.
So, yes, "royal gardens" and filled with slaves brought in from distant lands.
We don't know where that first "royal garden" might have been but archaeologists working in Iran may well have found it ~ and are working very carefully to recover every piece of information available.
Righto. The reason, of course, that so many species were domesticated in the Americans, as compared to the Old World, is that with the exception of maize (North America) and potatoes (South America) they weren't very productive in the old calories/acre test.
Since the native Americans were so much more "advanced" than Europeans, why didn't the NAs "discover" Europe and colonize it instead of the other way around?
I've read a great deal about the pre-Columbian history of the New World, and I'm perfectly in agreement that their achievements have often been overlooked, but let's not let hyperbole get out of hand.
While there were areas of what is now the USA where "civilizations" had sprung up, notably in the South and Southwest, they were at best at a stage roughly equal to that of very early Sumer or the peoples discussed in this article, which were 5000 to 7000 years earlier in the Old World.
No large domestic animals, no wheel, no metal (for utilitarian purposes), no writing. That's not an advanced civilization.
BTW, "migratory herdsmen" is not an earlier stage of life than settled agriculture, it's a parallel one. It's far more advanced than the hunter-gatherer stage and to be fully economically viable often requires a settled agricultural society nearby to raid, rule or trade with.