1914
I know it's a sort of a cop out answer, but there only really was one massive twentieth century war and it tripped off by a radical assassin and a German kaiser.
If I was to pick one of those dates, I have to pick 1939. By the time the betrayal of Czecks happens, things are getting close to the point of no return, but the official declaration that plunged Europe into war is in 1939, and it seems like the cleanest and neatest date to put there. Some radical scholars even argue against Churchill, calling him a war monger for declaring war on Germany, saying that if Germany had taken Poland, they would have been content and there wouldn't have been a war. When Great Britain and France got involved, that was the biggest escalation.
This question does introduce a wonderful point: There is a reason that World War II isn't called World War II in a lot of places.