Cos it’s a fantasy what-if sichewashunnnnnnnnn…!!!:mad::mad::mad::mad::mad::mad::mad::mad:
U mad Bro? 
He won’t be after the balloon goes up.
I doubt the war could start with A-bombs available because a heck of a lot of expensive research and development is necessary to make a working bomb; a lot of wannabees today still haven’t managed it. I could however see the knowledge of how to build a prototype “pile” in the public domain circa 1938-1939, if Leo Szilard had been able to interest anyone in his earlier ideas about uranium. If that had happened then the major powers would almost certainly have looked into it. The big question is whether Hitler would have listened to advice to delay the invasion of Poland. Even with a working reactor he might have been skeptical about “Jewish science”, and he was already insisting the war get underway even when his generals advised waiting a year or two.
Some of the constraints would have to be on the number of bombs available, as well as the delivery methods, otherwise it would simply revert to MAD.
One has to assume that with the development of the atomic bombs, the countries would have spent more on the delivery system, which would primarily be heavy bombers, unless we’re magically giving rocket technology and the cash to build them.
The problem is no only the design, but also the separation of uranium, as we can see in Iran.
In our universe, almost all of the major powers would not have been able to build the bomb because of financial limitations. In 1937, for example, the US have seven to eight times the industrial war materials capacity of Japan, with plenty of slack in the system, where Japan was close to maxed out.
However, if all the powers had the bomb in limited quantities in 1939, how would the decisions up to the war be different? Would Britain still provide guaranties to Poland against a nuclear-armed Germany? Would the US concede China to Japan or still continue with the oil embargo and other trade sanctions?
The US, with it’s huge economic advantage over the adversaries could afford to create more bombs and bombers. I wonder how Hitler and the Japanese leaders would have looked at the US under those circumstances. Would they have been as willing to risk destruction when the “moral weakness” would not be such a factor?
It’s worth noting that 1945-1949 the Soviet Union knew atomic bombs worked and had a substantial head start due to espionage. Yet it still took four years and at one point Beria accused the scientists working the project of faking results. I can’t see the Soviet Union having the bomb until well after other powers develop them.
Not only that, but the technology base changes too much to extrapolate much from our history. If you take technology up to 1950, then it’s not too far off from what was around in WW2, and you can treat a lot of stuff as no different. But if you’re talking 1960s or later tech, then you have better computing, jets, radar, rockets, tanks, submarines, and much more, and it would radically modify how anything plays out. The battle for the Atlantic, for example, will play out very differently if Germany starts with type XXI submarines (the first capable of operating primarily submerged instead of diving occasionally) instead of only being able to build 4 by 1945, and even more differently if they have late-50s nuclear powered submarines.
IMO if you’re postulating ICBMs and MAD scenarios, you’ve postulated such a different technology and societal base that you can’t do much real extrapolation from history.
Why would it make that much difference? At the outbreak of WW2, people expected aerial bombing to be about as effective as 1940s nuclear weapons were, and by the end of the war big US air raids did more damage than either of the two nukes did. If you’re talking about nuclear weapons on the scale of what was dropped in WW2 or what was around by 1950, and arsenals of a dozen or two warheads, I don’t think it makes any difference to that kind of planning (though attempting to control uranium supplies would become about as important as oil). Without decades of viewing nuclear war as the end of the world and seeing nuclear weapons as special, almost magical doomsday devices they’re just big bombs.