This means that they ate meat primarily most of the year, and in some places, as with the Inuit, they ate meat pretty much all year. And they were excellent hunters. Most of what we know about paleolithic people is derived in one of two ways. The first is by archaeology, where the remains that are dug up are studied. The second is by anthropology, where we study people who survived into the 20th century as hunter-gatherers.
A lot of what is found at dig sites from the Paleolithic is weapons, for example stone spear heads. They made lots of spears, both wooden and stone, although the wooden parts don't usually survive. Both homosapiens and neanderthalensis used spears to hunt medium and large sized mammals.
Atlatls were used as a means of extending a spear's throwing range and increasing the amount of force behind the throw. Atlatls have been used for probably 400,000 years, and would have allowed even a child to bring down large game.
Research at a site in Russia shows that ancient people could easily have hunted very big game like mammoths.
"Ethnographic sources and experimental work confirm that recent African elephants can be killed with spears or projectile points. According to Trilles (1932), Forest People from Gabon hunted elephants by sneaking under a standing elephant and thrusting a spear into its belly; the elephant could also be killed by arrows... According to Janmart (1952), the Ituri hunted elephants by creeping under an elephant and plunging a spear into its belly. The Ogiek people from Kenya hunted with dogs and used spears to kill elephants... Frison (1989) showed experimentally that Clovis projectile points used with atlatl and darts or thrusting spears can penetrate the thick hide of African elephants and inflect lethal wounds on elephants of all ages and both sexes. The hunting strategy should include several persons.
Comparison of the size of recent African elephants and mammoths shows that it is plausible that prehistoric hunters used the same techniques for hunting mammoths as recent hunter use to kill elephants."
So much for a lack of food. A large animal like a mammoth would feed a lot of people for a long while. Even smaller animals like deer or elk would feed a good number of people. In the winter, the meat would have lasted for a while, in areas where the temperature was cold enough to inhibit decay. And unlike fruit and vegetables, when the meat was gone, they could go and hunt some more.
Evolution has not had time to alter our genes to adapt to an agricultural life style. It has especially not had time to alter them to deal with the massive increase in sugar consumption that has happened since the early 1980s.