That's highly misleading. Pre-agricultural humans weren't some kind of noble savages, living in perfect harmony and balance with nature. They lived "sustainably" only in the sense that their environment killed them off at the same rate as they procreated, not of their own volition.
Between (and in defiance of) those two positions are some interesting ideas about sustainability.
On one end, "cavemen" are sustainable humans with implied cultural virtues. On the other, the pre agricultural equilibria is mostly about high human mortality and low population size.
At any given time though, people often had cultural understandings of natural ecosystems. We started being humans by living as part of such ecosystems, and undoubtedly both caused and witnessed all sorts of sudden changes and disasters... some linked to human activity.
If you live in an areas, and rely on plants, game and such... your culture is more likely to be "literate" in these things. Game can be hunted out, plants overharvested. A population surge in one species may deplete another. "Balance" can be restored, sometimes in a more or less beneficial way than before. These are all observable, and of great interest to people (those left) who make their living this way. The occasional and unpredictable flush of rabbits one autumn, is relevant to the life of someone who eats them.
