I believe the parking at the port opens around 10am and then you can start dropping off your bags and heading on upstairs around 1030am. I may be off on these times a bit and I would guess there are a few factors that may throw off the opening time.
Here is something I just found from a recent cruiser:
The port opens to incoming traffic at 10. If you arrive before the port opens, you will have to park off the property till it opens, so if you are in a taxi or limo, you do not want to do this. The counters open for check in at 10:30. Boarding is scheduled to start at 11:45.