If it was only that lax timing then it would have been much easier to develop the bomb. As I recall the window for detonating each plate in a spherical charge trigger is around 100nS, and even requires that the wires running from the electronics to the charges, be within mm of each other length wise, otherwise the speed of electricity in a wire becomes a problem with the charges being synchronised enough to form the right pressure wave on the pit.
The complexity of getting all of that right is why they struggled with the spherical trigger method for so long during the Manhatten project, and why the first bomb was the 'known to work reliably' 'gun barrel' design of the "Little Boy" weapon.