It's difficult to say really because football evolved from Rugby, which evolved from what we call soccer, so it gets kinda cloudy as to whether you're referring to football or rugby, but then if you're including rugby, you might as well include soccer too since that's where it all started, but that's not the very beginning either, you might as well go back to phaininda by the Greeks, the very very beginning.
Talking about American football, it was probably Walter Camp, since he's considered the father of American football because he's the one who redesigned the rules of the game. If you're talking about professional football, then it wouldn't necessarily be the first, but probably William "Pudge" Heffelfinger, as he was the first person to get a contract (for $500.00) to play professionally.