We have boarded as early as noon, some passengers have boarded by 11 to 11:30. If there are delays, boarding could start later. The latest I recall the doors opening for check in was around 12:30. It depends on when the ship clears customs. The longest delays are usually when they have a customs inspection.
In May, we got to the port around 11:30 and had to wait until 12:30 to board. Since we are so close, we usually leave home around 11 (arrive by noon) because we don't want to get there and wait around. We have VIP embarkation and want to get our lunch & DOD early because we have early dinner seating.
If you arrive between noon and 1:00, you should be able to get checked in and board pretty quickly. Lines can get pretty long, but they move well. I have read the lines are really short after 2:00.