I've heard of people boarding as early as 11:00. We got on later--about 1:00--traveling with a group who didn't want to leave too early! For our trip in June, we plan to be there around 11:00--makes the trip seem longer if you get on board earlier!
We got to the port about 1030am, unloaded the rental car and went inside. We had filled out the documents beforehand online so we didn't need to stand in the LONGEST line...We went right around that one and to the much shorter one. We were on the ship by 1115am! It was great too because it was our first cruise and we had no clue so we kind of walked around and got to know where everything was and then we stopped in the Windjammer to grab some lunch before heading to the stateroom. Checked out the stateroom and luggage was still not there yet, which wasn't really a concern and went to the pool deck to await departure.
Really beautiful and efficient. By the time we were out of port and in the open sea, we went back down to our stateroom and our luggage was outside our rooms.