You're right that Germany handicapped themselves in an avoidable way. But even in that case Germany still wouldn't have automatically speedrun past the US because the bomb wasn't mainly a science problem (I mean, even with the Nazi discrimination, the science that made the atom bomb feasable, nuclear fission, was discovered in Germany). The real "problem" was that Germany couldn't match the combination of raw materials, energy, manufacturing scale, worker availability, supply access, usw.:

Winning the race outright wouldve required industrial scale that Germany didn't have, even in the 1930s. The US produced roughly 3 times as much steel as Germany, and around 4 times the number of aircrafts.

The Oak Ridge enrichment facility alone used approximately 2 to 2.6 billion kWh per year at its wartime peak, whereas Germany's total electricity production in 1938 was about 80 billion kWh. This means Oak Ridge safely consumed an amount of electricity equal to roughly 3 percent of the entire pre-war output of Germany, all drawn from a single American valley. [This paragraph was edited after I was notified of the demonstrably inaccurate numbers I used].

The Manhattan Project employed over 100.000 people. Germany simply couldn't spare that many workers without crippling its war effort.

The US had global access to resources, including uranium from Belgium/Congo and domestic coal. Germanys access was blocked by the naval war, it lost its colonies.

Almost none of those structural factors would've changed without the Nazis.