In my experience, the wave motion is exactly the same each time the game is started. I’ve noticed this when I produced the videos of Physical Water Surface for my channel.
The explanation is this: The wave motion depends on the Game Time. The Game Time starts always with the same value when the game is started.
Please try this (with an unmodified version of Physical Water Surface): Load the DemoMap Level. Click “Play” to start the game and observe the motion of the boat, then stop the game after a few seconds. Then start the game again and observe again the motion of the boat. You will see that the motion is exactly the same.
So I think you don’t need to do anything, the waves are already the same each time the game is started.