@polyharmonic
About the only hope you've got of faster progress on nuclear tech is butterflying the barbecue of people and resources in WWI.
There was a bit of a pause in physics research from 1910-1930 where great work went on, but at a slower pace b/c other things were much closer to hand- chemical weapons and tanks and other stuff, even heavier-than-air aircraft were more promising than nuclear energy.
Keep in mind, everyone else except the UK is playing with anywhere from 1/2 to 1/20th the resources ($$$, tech, and people) that the US worked with in Manhattan project (and getting to crib from Tube Alloys' notes, mind).
The UK could probably have had a working nuke by 1940- IF they went full-on, didn't have the Depression or WWI casualties/debt hangover to clean up after.
Again the $$$ and human resurces weren't budgeted there.
You want to give up radar, jet engines and a ton of other things just to have nukes?
This ain't Civ IV son, where the tech tree's obvious and you're Maximum Leader able to get the ants working on whatever to the exclusion of all else.
What's the existential threat from 1920 on spurring this crash project?
The Germans? The Soviets? The Lizards from tau Ceti?
Say Italy wants the bomb from scratch in 1935. They couldn't afford sufficient weapons for a WWI army, much less a competitive combined-arms force against any competent European state.
That's why Italy had trouble with Ethiopia and no shot whatsoever solo against France. Greece kicked them out and Italy needed German help in both Yugoslavia and Greece to avoid humiliating defeat.
Trying to hide a serious nuclear research program would be impossible for Italy.
You want them to build nuclear weapons from scratch by when, 1980?
France, if it got the Dirac or Fermi or Einstein note in 1935 might have been able to put it together five, ten years after Manhattan/Tube Alloys working solo. They had uranium in West Africa and could possibly develop and test it in secret there or in Polynesia.
France had plenty of industrial equipment, universities (intellectual capital), and so forth. More with German, Austrian, and C Euro refugees)
Still, 1950-1955 before they build and detonate a working nuke w/o crashing their economy.
Japan would be about in the same boat as Italy. They aren't hopeless, just way behind and needing to develop Manchuria and Korea economically to where they weren't a drain on imperial resources.
The Japanese Empire wouldn't be in the economic or military position to develop the bomb until 1960 at the very least.
The wild card in this scenario is the USSR. IF they don't gut themselves with purges and then get the harrowing from Germany during WWII, would have ample resources to get the Bomb more or less by 1945 if they went flat-out WiTHOUT cribbing from the Manhattan Project via Fuchs and the Rosenbergs.
The problem ITTL is a few scattered A-bombs (20KT apiece) aren't the 10, 000+ city-killer 300+KT city-buster instant sunshine thermonukes via ICBM/MRBM maintaining the current balance of terror. We use nukes now, you're signing your own death warrant as well as nuking your enemy.
if it's the USSR vs the world in say 1950, bet on the world curb-stomping them conventionally until they can return the nuclear favor.
Problem with that scenario is that nukes become just higher explosives and aren't as taboo. More get used, folks discover radiation hormesis is a thing, and thus, there's survivable rad doses w/o developing a new limb or leukemia, and probably a bit more atompunk vibe going on (Wider usage, much greater comfort working with fissiles, etc etc.)
I'm not saying it's impossible for nukes to be around before 1945, but anything before 1940 w/o SOMEBODY spooking all concerned to get bigger firecrackers is bloody unlikely with a lot of distortion effects on scientific research, economic development, political priorities, etc.
YMMDV but that's my take.