Er, The Soviet Kilo class submarine had anti aircraft missiles since 1982.
I believe the Ruskies wanted to embarrass the USN anti sub forces.
Er...So in 96, a soviet Kilo class sub, shot a missile at a civilian 747 off Long Island. You said USN sub, but lets just go with your theory. Im fascinated now.
Any chance the sub sailed from a Nazi base in Antarctica?
Of a sort. Some were fitted with launchers for a navalized version of either the SA-8 or the SA-10. The were mounted on top of the snorkel mast and the sub had to be on the surface to fire them. Not very practical.