” the plume starts at water level.”
That’s cuz you’re watching from over the horizon.
As I watched the video from the original news program the plume is at the horizon but the telltale is the plume itself.
A SLBM breaches the surface and the engines fire. The missile rises vertical as it stabilizes itself and then orients itself. Once it has settled down it starts the pitch program to send it toward its intended target.
The vertical flight is only several hundred feet and you can see the vertical portion of the plume in the original video from the news station. You can also see the wider smoke base on the video where the engine start sequence initiated.