Yes, and the British were ahead. Churchill started the program with project Tube Alloys to be undertaken in Canada because Canada had hydro-electric power available to produce heavy water (D2O). Adolf Hitler was prejudiced against E = MC2 considering it to be suspect Jewish physics.
The WWII bomb project history prior to the Manhattan project is pretty fascinating.
Initially the first and most dedicated nuclear bomb project was the French. The French ministry of defence was approached by the Collège de France physicist Frédéric Joliot-Curie, who proposed that he might eventually be able to build them a bomb. This was back in 1938 or so.
So Jolliot-Curie got the comission, made the first controlled nuclear chain reaction in his lab, scored heavy water from Norway and Uranium ore from Belgian Congo, and looked pretty much set to go, at least as the early stages of development were concerned. As it was early days still, it was mostly about how to control the power generated by a fission reaction, but from the French Ministry of Defence's pov the goal of it all was a nuclear device eventually.
And then Germany invaded in the summer of 1940...
At that point the French physicists handed all the work they had done so far over to the British. The British integrated it with their own efforts and developed it all further. Eventually everything was all pooled wtih the American stuff and went into the Manhattan Project.
As for Hitler not "believing" in Einsteinian physics, I really don't think that's true. What happened in the 1930's was that a bunch pf opportunistic second-rate physicists launched something they called "Deutsche Physik", claiming the theory of relativity etc. was somehow erroneous for being "Jewish". They got some play out of that, but it's not as if Werner Heisenberg at al., the first rate minds, had any truck with that kind of nonsense. (The Jewish physicists forced into exile, like Lise Meitner, being a liability for Germany is another matter.)
The reason the Germans didn't get cracking at the Bomb was probably rather that the problems and costs involved were overestimated by the German physicists who would have been tasked with building the thing. The British had a bunch of the more prominent ones rounded up in a comfy villa just after that war's end, wiretapped 24/7. These printouts have been published after the war. The interesting bit is the German physicists' reaction to the detonation of the bombs over Japan; they were frankly astonished, and immediately began frantic activity, organising seminars and things, to try to work out how the devil the Allies could have accomplished that. They didn't really think it possible until it was done it seems.
(There seems to have been an allied agent sent to Heisenberg in Switzerland at one point during the war, with the task of feeling Heisenberg out as how far any German bomb-plans had proceeded. If they could be regarded as sufficiently advanced apparently he was supposed to kill Heisenberg on the spot. Fortunately for Heisenberg, it dawned upon the agent that the Germans had so far made more or less feck all to build a bomb.)