Maybe the point of divergence is WWII, maybe the 1944 election never happened and the election was delayed until WWII over. Given that it ended in Aug 1945 allowing time for primaries etc.. perhaps 1946 would be the earliest date they could hold it.
That's an interesting theory, but there's one problem with it (aside from the legalities of suspending an election, which I'm unqualified to comment on). FDR's Vice President between 1941-1945 was Henry Wallace, but FDR decided to replace him on the ticket with Harry Truman in the 1944 election. We know from a conversation between Debbie and Walken that Truman was President in the WWverse in 1945 and ordered the nuclear attacks on Japan. So for this theory to work, Truman would either have had to have been on the ticket in 1940, or FDR would have had to have gone out of his way to get Truman elected VP via Congress in 1944.