The nuclear bomb is a perfect example: It's actually a very simple mechanism, and the steps needed to refine the materials and make the mechanism are extremely well documented. However, the capability to actually reliably and safely make it is quite difficult.
If you want a real nuke today - the thermonuclear fusion bombs - you're going to be missing a lot of parts that aren't in the public documents.
This is actually proving my point.
For the simple bomb you mentioned, you need U-235, in high quality. That's actually very difficult and dangerous to refine and manufacture. It's time consuming, expensive, and requires bespoke process across multiple disciplines. Even today, some nation-states struggle with the process.
This kind of science is almost inherently international, and I don't think they could possibly keep up "keeping quiet" all the potential successes.
That said, if there was one, I do think they'd at least try and fail.