Nukes were more as you described. They were all based on what the math said, but no one had worked out the exact details and this was the closest to "physics = magic“ that humans had come to. It speaks to America's trust in science that the Roosevelt administration actually believed that slamming 164 pounds of uranium (then a metal of no great renown in popular culture) together would do more damage than 32,000 pounds of dynamite.
That and convincing them that it was worth 2 billion dollars, getting the treasury department to fork over 5,500 tons of silver, using one seventh of all electricity in the United states (iirc over 30% the total electricity production of the third reich during its total existence), and the minor detail of building a bomber to carry the thing, at the cost of three more billion.
The nuclear bomb project was not a trivial one. There's a reason the British bowed out and gave all their information to the US.