It's about 'when' more than anything. We live in a world today with mostly free information sharing on most scientific subjects. But picture a time when cutting edge science like the nuclear programs were veiled heavily in secrecy. Every single development took time, effort, work, science. And the result is... an answer that can probably be written down in a single piece of paper. Easily shared.

The USSR would have developed the same bombs eventually, but not as quickly, I would guess.