This question gets asked at least 1 or 2 times a week and every time it has the same answer: it is impossible to say but likely never. It's impossible to answer because we frankly don't know everything about everywhere and about all people across the world for all time. In fact, we have lots of blind spots. Secondly comes with the definition of "war". Would you consider the Cathar Revolts a war? What about isolated and staggered viking raids on the coasts of England? The answer of what constitutes a war and what separates it from a conflict or a revolt or whatever or if they're all intertwined is critical to answering this question but is also entirely arbitrary. I mean we have laymen to this day who still consider Vietnam not a war since there was no formal declaration from our government despite 50,000 Americans and by some accounts over a million Vietnamese dying. Would that count?

The further we go back the more impossible this question begins to answer but the shorthand is that from what we do know about history and the peoples across the world it's that we've always been fighting over something and there's no reason to assume that wasn't happening somewhere throughout time. Also, brief consideration of your statement "the start of civilization" -- that's stepping on some toes around here as that's an incredibly loaded and also vague term :)