That is not accurate. The right to acquire property by conquest was well established in English common law long before there were any American colonies.
"Acquire by conquest" is very different than "taking over abandoned or unoccupied land." Someone has to actually
be there in order to be conquered. Other than the first waves of occupants, land wasn't "unoccupied," i.e. it's been "conquest" for tens of thousands of years. In the agrarian eras and after, territories were not raided because there was nothing there, but because people and crops and supplies could be seized.
It was pretty much only the Americas where land was seized using the rationalization that the land was "abandoned" or "not in use," although it
was being used, cultivated and lived in by indigenous tribes.
Of course. That is just what has been done with large areas of Antarctica.
Unless it isn't. Various nations claim control of Antarctic territory, mostly based on sheer declarations of swaths of land they didn't literally occupy, while the Antarctic Treaty declares it as a "scientific preserve."
And no, you can't just row up to a section of Antarctica and make a land claim that will be recognized by any government.
A person may acquire another person's land by adverse possession, but only under certain conditions. Someone would have had to been occupying your land openly, with your knowledge and against your interests, in a way that excluded you from it, and have done it continuously--usually for twenty years.
That doesn't answer my question.
Again, you claimed: "Where no one else is occupying land or otherwise making use of it, anyone who wants to has a right to that land." Why would this apply to land occupied by indigenous territories, but not to modern land ownership?
E.g. if I have a 20 acre estate, and I'm not actually doing anything with 10 acres of it, does that fact alone give another person the legal or ethical right to seize the land? If not, why not?
Or: The Powhatans outnumbered the Virginia colonists for decades. Did the colonists only "earn" the right to seize territory when they became more numerous, or the population became more dense? Or when their crop yields were greater than the Powhatans? Would it make sense for the English to approach the Powhatans and say "there are more of us, therefore this land is no longer yours" or "we grew more corn than you this year, therefore we're taking all your land."
By the way, most tribes (especially on the East Coast) were not nomadic by the time the Europeans showed up. The Powhatans had many settlements on what we now call the Virginia coastal areas. Many colonists tried to seize territories that were settled by Indian tribes. They relied on military force to kick the indigenous tribes off their territories. Does that sound like an instance of people who had no claim whatsoever to a territory...?