Digging until you can't dig anymore due to floating is what I used as reference. You may get away with a little less, but not very much.

The amount of clearance for the mast depends on sea conditions, but these are a couple of my covered docks:

https://steamcommunity.com/sharedfiles/filedetails/?id=2624259961

https://steamcommunity.com/sharedfiles/filedetails/?id=2616846356

The last one is now filled in with rock, since it was in the old mistlands, and I can't find a picture of my main (plains) dock.

In any case, I think you can get an idea from these pictures what you should need. I think they're both about as high as you can build a roof without aid of reinforce beams. You may get away with less, but the mast might hit the top in rough seas.