When I say "Indirectly" I mean without the use of some sort of document that points to an old census that was done by the time to count the population. What I mean, is what lines of thought and evidences can be used to estimate populations from natives from the Americas, or from barbaric populations by the times of Rome, etc, and how safe are specialists are that a certain number might be close to the real one.
Full disclosure, I'm not an archeologist. But I am a Classicist, so I read bout this stuff all the time.
One interesting "direct" way of mapping ancient populations is via pollen analysis, see here. The idea is that you can essentially track population growth and distribution by figuring out the quantity and types of the crops people are growing. Obviously, there isn't a way to fact check this with 100% certainty.