Early in the development of the Polaris missile system, there was a lot of work on launching a missile from underwater.
Polaris was a nuclear deterrent to rapidly launch multiple missiles from a fully submerged submarine. Staying submerged until a boat-load of launches were complete was a key goal: the boat was to be very difficult to track and destroy even as multiple missiles were rising from it.
Direct launch from the missile tubes was known to be infeasible without destroying the boat due to the heat and pressure of the launch. Unlike travel in air, where the plume can rapidly expand away from the missile and platform into the air, the missile tube and surrounding water would confine the exhaust gasses so that pressure and temperature would rapidly rise toward the rocket engines chamber pressure and temperature.
The project attempted to launch using a much smaller “extractor” motor, but this was also not successful. Designing a tube (to protect the sub) and aft missile end (to protect the missile during launch, which was the point after all) was not compatible with an extractor motor that could lift the missile to the surface.
In the end, they went with an air-powered push to the surface, followed by motor ignition when the missile has cleared the surface.
Early Polaris launch video
There are persistent rumors that certain Russian torpedoes use rocket motors for propulsion. Torpedoes are small, tough, and their weight isn’t so important.
Polaris and it’s follow-ons are ballistic launchers; they don’t go to orbital speeds. It seems hard to believe that a rocket for orbital use could be built tough enough yet light enough to launch from under water.