It would be longer for the United States, but to say the Germans would be the first to produce the nuclear bomb and use it just is impossible.
After some digging for a thread on SpaceBattles War Room, someone posted the situation Germany was in and they were in no position to try and produce something they had no means to create. If you want the source, here's the link to the PDF to the German reaction of the nuclear bombs being dropped.
The United States had the resources and economic capacity, but the Germans didn't.
Wasn't Einstein the one who convinced the American government to start the Manhattan project in the first place though? If the Nazi don't launch mass anti-Semitic attacks in 1933 like they did OTL the US government might not view the atomic bomb as a real military concern and focus on conventional weapons instead.