It seems the hominids at Gran Dolina had a solution to the problem you’ve mentioned above.

A close look at the fossils found at Gran Dolina from 800,000 years ago reveals a startling story: these hominids were butchered by other hominids. Both the human and animal bones have similar markings on them that could only have been made by stone tools. Using this evidence, the researchers who discovered these fossils argue that these hominids not only ate other mammals but also other humans.

The hominid remains were jumbled together with several thousand bone fragments from other mammals. Many of the bones—human and nonhuman alike—have marks that could only have resulted from being chopped and scraped with stone tools. Scientists working at the site suggest that the way in which the bones were cut, twisted and broken indicates that both the meat and bone marrow were eaten.

Modern humans have practiced cannibalism—but only very rarely. Researchers have no way of knowing why the early humans at Gran Dolina ate others of their kind. A rich diversity of animals lived at Atapuerca during this period, so the hominids probably did not lack food and turn to cannibalism to meet their nutritional needs. Instead, the cannibalism seems to have taken place over a long period during which the hominids of Gran Dolina made human flesh a regular part of their diet.