I wonder if you could sink a very buoyant rocket to the bottom of the ocean with a weight, and then fire up the rocket engine as it breaks through the surface o

I wonder if you could sink a very buoyant rocket to the bottom of the ocean with a weight, and then fire up the rocket engine as it breaks through the surface of the ocean with a positive upward velocity. Presumably drag in water is the biggest issue, which would be somewhat mitigated by the aerodynamic shape of the rocket. I wonder what is the maximum theoretical exit velocity from the ocean, using only buoyancy as propulsion.