All of the astronauts that have ever walked on the surface of the Moon have been male. Find a plausible way to get a woman there in the later half of the twentieth century. It could be from any nation in the world.
What if instead of the Nazis launching Operation Barbarossa first in the spring of 1941, the Soviet Union instead launches a counter attack intent on removing Germany as a military threat to itself and to spread influence across the region.
What if Robert F. Kennedy was not assassinated in 1968 and ends up losing the Democratic nomination for the White House just months later. What does he do with the rest of his life if he does not run for elected office again?
Have the Japanese launch a majorly successful raid along the western shores of the United States sometime in 1942 using naval and air forces. It must bottleneck war time production for months and leave a deep psychological trauma on the American people.
Make the 1996 movie Independence Day the first film in a franchise that spawns sequels, television elements, spin-offs, and more that is much bigger than what it was OT.