What if Hitler had realized he was going to lose earlier in the war and hadn't killed himself, but instead had escaped from Berlin/Germany?
Perhaps this is what happened...
He did realize in late Spring 1945 that Germany was about to be defeated. This why he faked his own death (leaving a clone of himself in the Berlin bunker), and escaped to the secret Nazi base in New Swabia -
http://en.wikipedia.org/wiki/New_Swabia
After this fact emerged, the US Navy sent Operation High Jump to the Antarctic in 1946-1947 to drive the nazis out
http://en.wikipedia.org/wiki/Operation_High_Jump - but by this time they had already mostly escaped to the moon. Nevertheless the Nazi base was hit by perhaps a dozen atomic bombs - which in retrospect was a mistake, seeing as this action was unnecessary and resulted in the release of the frozen giant sea lizards (which of course remaining a maritime hazard to this day).
Out of sight, out of mind, and nobody worried about the lunar Nazi issue until the early 1960s. JFK was however shocked by these facts when he became President, and this why he announced the goal of reaching the moon within a decade. Of course once the Apollo program had been initiated, JFK also faked his own death (using the capturing Nazi cloning technology), and we now know, personally commanded the secret Apollo 18 mission to the lunar far-side, which of course finally eradicated the lunar Nazi menace.
(Sorry I couldn't resist, Hitler escaping to a secret base is of course an over-used staple of fiction)