It's possible. Actually way more feasible than the vegan diet, as ruminant animals have all the needed nutrition from plants. However, humans have regained the ability to digest plants after the ice age gave way to agriculture. Obviously, the ideal diet for most is just to eat meats and vegetables, no vegetable oil and sugars.
I'd only recommend the carnivore diet to those with dietary issues like IBS.
There are plenty of tribes that were carnivorous.
>https://carnivoreaurelius.com/beef-liver-tribes/>inb4 plebbitors going "UHHHHHH, SOURCE? BARK BARK MASTER GOLDBERG TOLD ME I CAN ONLY LISTEN TO SOURCES HE LIKES!" 
