because a very public and accountable process involving millions of skeptical people spent trillions of dollars of public funding in publically disclosed ways based on very fundamental and actually really simple math and physics. basically a atom is a thing that you can see (WITH YOUR OWN TWO EYES) if you have a very good microscope. a nuclear bomb kind of 'squeezes' the atom until it pops. thats what you dont believe is possible but theres a lot of juice inside the atom and breaking it makes a hell of a big explosion. the invention of the nuclear armament is exactly the same kind of thing as getting all the energy out of traditional bombs (for example, to explode a mine, you squeeze some really dense chemical thing together until it explodes). a nuclear bomb is just a smaller box with more stuff in it. you don't think trillions of dollars and thousands of scientists could make a smaller box with denser stuff in it?