1904 with the Russo Japanese war. France and Britain were allied with Russia and Japan respectively, and you'd probably have all of Europe joining in the fight in order to reap as many benefits as possible.
WW1 should have been a war limited to Austria-Hungary and Serbia, instead a long network of alliances turned into the bloodiest European war up to that point. A similar prospect could have occurred with the Russo-Japanese war if Britain and France kept their alliances.
Theodore Roosevelt also happened to be President at this point in time, and he happened to be the last US President to romanticize warfare as a bit of a gentleman's game, so for the Pride of the United States (and the wealth of the British/French colonies around the Americas and the Caribbean) the United States may pick a side.