This would be a good way to go if your book wants to highlight the injustice of racism.
Change something in WWII relating to the treatment of the Jews, which worsens antisemitism worldwide. As such, nuclear bomb potential is rejected by everyone (instead of just Germany) as "Jewish physics".
Antisemitism never dies
Remember: being a Jew in 1940 was not a bed of roses. Blatant antisemitism existed throughout the world and was just a normal part of life. And believe you me - America was completely capable of that level of racism at that time; they were already doing it to African Americans. But in our world, Germany took antisemitism to its final conclusion. The horrors of what this actually looked like shocked people out of it.
Here this doesn't happen for some reason. Say Hitler actually "crunches the numbers" and realizes the burden to the economy of a) operating massive concentration camps, and b) removing many highly effective workers, scientists and businessmen from the economy, will break the German economy and lose the war.
Now, Germany does NOT commit unspeakable horrors against Jews, they just use media manipulation to notch up antisemitism all over the world. The Allies arrive in Germany and find no Shoah, just baked-in German antisemitism that looks a lot like the antisemitism they have back home, just done a little more thoroughly and efficiently, but while still keeping the Jews in the economy. The antisemitism they find makes sense to them and many countries actually copy the techniques.
The upshot is that at war's finish, antisemitism is alive and stronger than ever.
In real-world Germany, nuclear research was rejected for years as "Jewish physics". That set them so far back that they never got near the Bomb. This continues worldwide: nobody can get funding to research it; merely broaching the subject raises questions about your parentage.
Getting bomb material is hard...
Let's review how one obtains bomb material. There are two branches, both starting with natural uranium. Uranium ore has a bunch of other crud in it; that's easy enough to separate to get pure uranium. But uranium itself has two isotopes: 0.7% is U-235 and 99.3% is U-238. Now there are two branches to a bomb, both staggeringly expensive, Manhattan Project level, budget-busting, large-state commitments:
The Oak Ridge path: separate the isotopes of Uranium to get the directly fissile U-235. So you are taking 25,000 pounds of U to make 141 pounds of 80% U-235. With only 3 atomic weights between them, that's biblically difficult. A lab could do a few atoms at a time - but you need 16 million billion billion atoms. The problem is scaling up; you just need a whole lotta machines. This is why we get excited about Iran getting centrifuges.
The Hanford path: Inside a reactor, neutrons will hit the U-238 and turn it into Pu-239, which is also fissile. However, neutrons will hit the Pu-239 and turn it into Pu-240. Pu-239 is great for bombs but Pu-240 makes it useless for bombs. And with only 1 atomic weight between them, forget about it - ain't gonna happen. So to get Pu-239 and not Pu-240, the exposed fuel must be exposed only for a short time, then removed, then Pu chemically separated from U. Which is easy enough; the problem is your yield. You're leaving the fuel in the reactor for such a short time that you have to process a staggering quantity of fuel to get a little bit of Pu239. But this chemical separation scales much easier than the Oak Ridge path.
Neither of these giga-projects is going to happen given that you can't even talk about the science without being blacklisted.
... But nuclear power is easy.
All you need is ordinary mined Uranium (0.7% fissile U-235). This is obtained via normal mining techniques; nothing special to it. This is probably already happening, since uranium is a rather useful metal for things like aircraft ballasts and anti-tank bullets. So the only thing that changes is that somebody assembles a big pile of it, inside a pressure vessel, on purpose.
In fact, two reactor types are already sized to be able to accept natural uranium fuel loads: CANDU I and RBMK. And they're operating right now in the two large arctic countries. BWR and PWR/VVER can't, but that's only a sizing issue.
This works perfectly well with natural uranium. In fact, the abundant U-238 will capture neutrons and turn into Pu-239, 240 and 241. All of them are useful reactor fuel. Further, where there's uranium, there's thorium; Thorium-232 can do the same trick; it picks up neutrons and becomes fissile U-233. The reactor can be tuned to make more fuel via neutron capture than it consumes in U-235, this is called breeding. So the concepts of natural uranium reactors + breeding fuel can take civil nuclear reactors rather far indeed, without delving too deeply into the impolitic "Jewish Physics" and the brobdingnagian problems of refining bomb fuel.
And the world is satiated with this approach to nuclear power.
Even if the bomb is discovered in theory, it is taboo
If the possibility of a bomb is discovered, the antisemitism bleeds over to the very notion of developing and using such a bomb.
Governments are quick to sign pacts that such weapons will never be explored, just as they have already agreed regarding chemical and biological weapons. Given the Manhattan Project difficulty of doing so and the large footprint that would make on both land and economy, this becomes easy to enforce.
Perhaps, somewhere, a civil reactor has already blown up and contaminated a large region, and so they know how horrible that is. (mind you, bombs are orders of magnitude less toxic than reactor accidents, downtown Hiroshima is a bustling city... but people couldn't possibly know that at this point).