Not sport in the sense of exercise purely for the sake of burning calories, but sport in the sense of fitness display for status, bonding through teamwork and practice for warfare, definitely. The amount of calories and protein that can be achieved from hunting large game is just far too low compared to the same amount of effort and risk expended on trapping, fishing and gathering.

Of course humans were eating meat in prehistory, and more than once agriculture began. But we make art of the ideal and aspirational more than of the everyday.