We are also cruising on May 1st on the Dream.
According to Carnival, Embarkation begins at 12:30 P.M. They will not begin before that time. Your patience will be rewarded once to get onboard! 
We are staying at the Radisson the night before and have shuttle reservations for 11:30 A.M. to go over to the port.
Carnival suggests that you not arrive real early to board because you will wait. Remember all previous passengers MUST be OFF the ship before the new passengers can board. This can be a long process.
For complete information, go to the Frequently Asked Questions on the Carnival Cruise site. There is a detailed section - Important Embarkation Arrival Advisory and Embarkation Process that will answer your questions.
Let's hope for calm seas and blue skies!
