First, let's define war as a prolonged inter-group conflict, as opposed to a single murder, raid, or other event in which death occurs by human action. There needn't be nation-states and official declarations, but war is more than one or two people killing each other. It also doesn't need to be defined by battles or dedicated soldiers: as you can see from the last 100 years, the nature of war can change (compare WWI, Vietnam, and the Iraq wars, with regard to goals, order of command, fighting forces, civilian involvement, etc).The first archaeological evidence for war is the Jebel Sahaba collection, a group of skeletons from Sudan from 13,000 years ago. These skeletons (which I've seen up close!) have numerous cut marks from weapons and stone arrowheads embedded in the bones. These injuries occurred over a period of many years, indicating a prolonged conflict. More about Jebel Sahaba:Sophisticated stone weapons such as spear points, and arrowheads have been around for much longer, and just plain rocks and clubs before then, but there isn't evidence that they were used in war as we'd define it. To have war, you need to have humans capable of group identity and thus inter-group conflict. If we pick roughly 50-100,000 years ago as the time when humans started to look and act like humans today, you could have those. There also needs to be a reason for war: in the Jebel Sahaba case, resource scarcity at the end of the Ice Age has been posited. I mean, people could just have decided to spend a bunch of time and energy killing another group because they didn't like them very much, but resource scarcity is more likely.However, this is also ignoring all the other Homo species who clearly had culture - yes, Neanderthals had culture! - and thus might also have had war.