In terms of diet, the researchers say, there's no one answer to that question. What hunter-gatherer populations eat - and most likely ate in the past, too - varies so widely that, they say, "the idea that there is one true, natural human diet to which we might all aspire is negated by the incredible variety of hunter‐gatherer diets recorded by early ethnographers and researchers today".
Many populations eat, for example, high amounts of carbohydrates as staple foods. "Meat‐heavy, low‐carbohydrate diets may have been the norm for some hunter‐gatherer populations in the past", say the researchers, "but many small‐scale societies, including those with excellent metabolic and cardiovascular health, eat diets that are relatively rich in carbohydrates and (in the form of honey) simple sugars".
What hunter-gatherer populations have in common, though, is that they all eat a mix of plant and animal foods - no vegans here - and they do not eat any highly processed foods. They might be eating carbs, but they're in the form of tubers, not Twisties.
They also notably have high levels of physical activity; hours a day in many cases, often at low-moderate levels of intensity. Interestingly, this doesn't necessarily mean they expend more energy than we do - but it's still associated with their remarkable health.
Also worth noting: the other aspects of hunter-gatherer societies which we also value, and contribute to better health: close friendships and family bonds, low levels of social and economic inequality and lots of time spent outdoors.