Assuming that the earliest possible date for atomic weapons (proper ones, not "dirty"bombs) is likely to be the mid 1920s, your challenge is, with a post-1900 POD, to either delay WWI or propose an alternative "Great War" with similar charateristics prolonged stalemate, trenches, widespread shocking use of modern weapons like MGs, gas, flamethowers, aircraft, etc.) taking place in the 1920s. (1930s would be OK, but 1920a is better.)
In any case, the Great War should end in the use of atomic weapons. The more used and the wider spread, the better.