That is a very interesting speculation. But vast areas of the world even today have virtually no population at all. The "# per square mile" is rarely reported as zero, but in reality it is very close to that. Much of the desert. Most of the high mountains. Virtually all of the seas.
Southern Africa was virtually empty when the Dutch landed there in the 1600s as traders, then along with the French Hugenots as refugees from the religious persecution going on in Europe. There were no blacks within a thousand miles to the north, and only a very few very primitive aboriginals. Not nearly enough to call that vast area "occupied".
When America began filling with Europeans the average population per square mile was clearly near zero. In no sense of the word were there enough Indians present to call America "occupied". (Revisionist history notwithstanding --- and no, you can't have ALL of western america as your own just to graze some mangy buffalo. {ggg}. The railroad is coming through!)
When Leif Erikson landed in Newfoundland ~1,000 AD he was met by local Indians. That figures, since this was at the waters edge that's where the few Indians would be found. But there were nowhere enough Indians present in North America then, or later, to in any sense call it "occupied".
Moving back in time, I wonder how many people were in western Europe around 600 BC when the Celts moved north and westward out of the region of the Caucasus? I haven't seen a number, but think we make a mistake to think in terms of todays crowded Europe. After all, the action at that time was virtually all in the region of the Med. and the warmer climes.
Was Europe then like Southern Africa, or America only 400 years ago? Pretty much empty. Was it like North America 1,000 years ago, virtually empty? Was the area of the Ukraine virtually empty, like the American west only 200, or even 100 years ago? The Celts had not yet left northern Iran/Iraq and passed through the Ukraine to settle and dominate Europe as they would do in the years following. Maybe, like their European offspring settling America, and their European offspring settling Southern Africa, they had no virtually one to "displace" when the arrived?
If you read the reports of the early Spanish explorers the American continents had a goodly sized population, the Anastazi were driven out by climate change, for example, small pox did a number on the rest.
East Africa, the Nile basin, and the area below Lake Chad down to Angola had a fair population. the Middle East, Asia Minor, Iraq and Afganistan. were heavily populated. Climate changes have converted some areas that were inhabitable to areas that are uninhabitable.