The explosion we see in the game is merely the launch point of the bombs that closes up to way to the underground. So, that explosion was survivable with all that gear he was wearing (even safety goggles)! As for the fall? Well, Cid probably fell somewhat into the drafty thingy that helps airships lift out of the underground. Why else is that weird crater there? So he sailed on that and while I am sure the landing sucked, it wasn't fatal.

Myth: CONFIRMED