One question I suspect the archaeological evidence is insufficient to answer is how far from the last village/roving band of hunter-gatherers the next band into the wilderness would settle. When you broke off would you stay within a day of your old village or would you walk hundreds, thousands of miles before stopping, completely alone?

As far as the mindset goes, I’d say keep in mind that when Europeans landed in the Americas and Australia, they considered those continents to be “empty”, free for the taking. Their world may not have been so different from the first human to walk out of Africa.

1491 by Charles Mann goes into this a bit. Some estimates put the die-off of aboriginal North Americans at 90% from the arrival of Europeans (in ~1500) and the early permanent settlements (Jamestown was in 1607).

The first descriptions of what's now the US east coast from explorers describe coastlines lined with fires as far as the eye could see, and suggested a fairly densely populated continent.

The descriptions from the early settlers (as you've noted) describe a loosely populated land of "savages".

I've always considered the 16th century a time of essentially apocalypse for North America. Imagine what would happen to our society if we had a 90% die-off over 100 years; even in the modern era we would probably find ourselves regressing to "savagery".

Oh, I'm not talking about the "loosely populated" part. I'm referring to the way that they by and large didn't really consider the inhabitants to be "people". Into the 20th century they were largely denied agency by the colonists, and in the 21st century we still displace Native Americans with roughly the same sort of discussion we have about disturbing turtle populations.

I don't think 16th century Europeans considered the Americas any more inhabited than the Moon. Native populations were just another natural resource the New World was teeming with, not "people".

If you look at it, that kind of humanism (where the distinction between "humans" and "not humans" is more important than the distinction between, say, "Christians" and "not Christians" wasn't in vogue in the 16th century. 16th century Europeans sent enormous numbers of missionaries to the Americas with the aim of converting the natives; they wouldn't have done that if orangutans were the prevailing primate on the continent.

An oversimplification perhaps:

https://en.m.wikipedia.org/wiki/Valladolid_debate

Not that practice matched theory but...

In some cases they actually were empty. Because all the inhabitants had recently been killed by diseases spread by the Europeans. One proposed mechanism for this is that infected pigs roamed wild "ahead" of the colonizers, killing the indigenous population.