The best clue is the gamma ray burst the a nuke gives off. We have satellites that would spot an air burst nuke in about 3 seconds.
The telltale would be a double flash, these typically detected by a specialized photometer known as a bhangmeter. Only an atmospheric nuclear explosion causes this kind of double flash. These instruments were carried by the Vela Hotel series of satellites tasked with detecting atmospheric nuclear tests. It was one of these satellites that detected an “alleged” test off of South Africa. I do not know if such instruments, or there successors, are still in use.