Maybe with heavy hacking, but not ready-made, at least that I’ve found. Certainly don’t seem to be any distros (in the casual searching I do periodically) that focus on 1-second boot times out of the box.

You might like https://www.benjamin-schieder.de/nethacklinux.html

Replace nethack with your favourite editor, and it might just work. (Well, also replace the floppy disk with something faster.)