There’s a way to prove it; we know how quickly pain signals propagate through our nerves and how quickly nukes disintegrate matter. The degree of skepticism you’d need to be uncertain about it would cause you to need to resolve solipsism before you allowed nukes to even exist. There’s a certain radius within which, if you don’t have sufficient shielding there’s no possibility of pain. There’s another smaller radius for which no amount of shielding will change the outcome.