Primitive humans were at a distinct disadvantage in a world of lions and hyenas. In a land ruled by fang and claw, early humans were unarmed. Also, humans seemed to lack the basic strength and athleticism necessary to compete on the savanna. Humans are slow runners being much slower than both their predators and their prey. Humans can climb trees, but not very well. We could never catch a monkey in the treetops. We can swim, but not very well. We cannot fly at all, putting the skies off-limits.
But even so, it is likely that homo habilis, the first tool users, were more scavengers and gatherers than hunters. The bulk of food intake for all primates is gathering, and early humans would follow that pattern.
Habilis became skilled scavengers, giving them an advantage over other primates. They found a way to take sustenance from recent kills even after these kills had been worked over by lions, hyenas and even vultures. Humans were able to use rocks and large bones to crack the skulls of the kills to extract the brains. Also, using the same techniques, humans were able to crack the bones of the kill to extract the marrow. Both the brains and marrow were rich in fat, calories and proteins. And eating fatty brains provide nutrition for growing fatty brains.
And then, of course, there is tool use. Tool use results from the synergy of bipedalism, binocular vision and opposable thumbs. Habilis would have begun by throwing projectiles, sticks, rocks, bones or whatever was at hand. At first this would have been mostly a defensive response to nearby predators. Even a lion would run away confused after being pelted with rocks from a primitive human pack. Later, as their skill levels and coördination improved, such pelting could take on an offensive role as well. A well thrown rock could kill an animal, predator or prey, by a well-placed blow to the head.
The next step in tool use would be a sharp stick. A sharp stick became the missing claws of the humans. Even a charging lion could impale itself upon a sharp stick wielded by the early humans. And the nice thing about using sticks is that even if it is broken or lost in combat, the human remains uninjured and can continue fighting with a new stick.
The next step on the evolutionary ladder was homo erectus. Erectus taller than habilis and with a larger brain size (900 cc vs, 440 cc). While the skull of the erectus had ape-like features, the rest of their skeletons were very much like ours. Erectus was the first species to travel out of Africa, ranging as far as Indonesia.
Erectus were also pack hunters. Humans resemble chimpanzees and bonobos in their basic morphology, but resemble wolves in their social structure. Pack hunting, as displayed by lionesses on the savanna, provide a distinct advantage in hunting prey, especially the larger species.
Humans do, however, have one athletic advantage. We can run for long distances. Other predator species can run very fast in short bursts, but any long distance running is out of the question. Erectus had the ability to run down and exhaust their prey. This form of hunting can still be observed in Africa today. While our bipedal design makes running very slow (Even my little Yorkie can run circles around me), our design is very efficient for distance running.
Walking upright uses one-fourth the energy than a chimpanzees four-legged gate. When you watch a chimpanzee walk it looks awkward with too many moving parts and too many wasted motions.
Other savanna predators tend to overheat easily. This forces them to rest after only a few minutes of exertion. But our hairless bodies enable us to shed heat quickly. Our bodies are long and lean and covered with sweat glands. We have a high ratio of skin area to body mass. Also, our vertical posture means that we absorb less heat from the sun while running. All of these things help us to exert ourselves for long periods of time without by dissipating our body heat quickly and efficiently.
Distance running, combined with pack hunting, does provide us with at least one effective hunting technique.