Oh, I just thought of a really cool setting.
Seeing how the Predator is such a flexible and versatile character who can fit in any setting or crossover and make it good.
Why not have a story of one hunting during prehistoric times? Like have them hunt Neanderthals and note differences among the human species. A good setting would be during or just after the Toba Eruption 75,000 years ago, there'd be so many different species of human to hunt in a very deadly environment ravaged by a super volcano.
Kinda like how one of the stories here took place during Hurricane Katrina. When Toba exploded, it nearly rendered humanity extinct. That'd be a cool setting, and because anatomically modern humans also existed in those times, making a character in that setting shouldn't be too tricky.
If you find any authors who are huge paleo enthusiasts, they should give this a try.
Speaking of which, I think someone noticed one of the skulls in the camp in "Predators" looked like it belonged to Homo erectus or another one of these really archaic hominins. It really gives you a glimpse on how old the Yautja are and for how long they've been doing this. Rage War loved reminding us of this fact that Predators are primordial beasts.