Isotope analysis of bones and of mummy tissue can pretty accurately indicate the nature of the diet people ate. Hunter gatherer populations, which ate almost exclusively meat, were taller, show no signs of bone malformation or dental caries, and no skeletal signs of other diseases. Populations that adopted agriculture and ate a plant-heavy diet, such as the ancient Egyptians, are shorter, have bone deformities, show evidence of caries and gum disease, and show other signs of ill health, including central obesity (as depicted in sculptures) and other signs of metabolic disregulation.
The conclusion is that our ancestors ate a high percentage of meat in their diet, if not exclusively meat, for most of human history (agriculture being a comparatively late developement); this is confirmed by the fact that a number of isolated tribes are documented to have been eating almost exclusively meat at the time of first contact, relying on plant matter for food only in times of famine. The relative fitness of the meat-eating Maasai in comparison to their mostly vegetarian neighbours, the Kikuyu, was documented in the 19th century by British colonial medical officers. Stefansson and others documented the Inuit diet at the turn of the 20th century as being exclusively of meat products, and Stefansson proved the point by joining with Andersen in their famous meat-eating diet in 1927-28.
The average life-span question is confounded by the childhood infectious disease issue, plus the lesser ability to treat injuries. However, populations such as the native tribes of the Great Plains of the American midwest were noted for their high percentage of centenarians (before they adopted the white man’s diet, of course), and this would tend to indicate that provided one survived into adulthood, life expectancy was high on a mostly animal-food diet.
I’d say that the evidence that a proper human diet contains a high percentage of animal-sourced food and very little plant-sourced food is pretty convincing.