The Manhattan Project started in 1942, was penetrated by Soviet spies no later than 1943 (Klaus Fuchs), and was known to the whole world by 1945. It's not a great example of extended secret-keeping.

According to documentaries, there was a whole army of spies.

From memory, one of the most important was a quadruple spy - the German gaseous diffusion expert was working for the UK, USA, Germany and Russia.

When FDR told Stalin about the bomb, Stalin just said, "Thank you."

You just need to keep it secret enough to hold out until the declassification of the documents a decade to 5 decades later.