Embarkation normally begins around noon. In typical Port of Miami fashion there are several thousand passengers lined up early to get aboard. It reminds me of kindergarten when everyone tries to get on the school bus first so they could sit in the front seat.
After a very long session of pushing, waiting, cursing, shoving, clawing, threatening, and complaining, everyone manages to get aboard. Lunch service, buffet, and BBQ all begin at noon.
If you would like to have a civilized start to your cruise, skip the transfer, go to a nice hotel or restaurant for a leisurely lunch, and show up at the Terminal around 3 PM. There will be no lines, no waiting. You can stroll right onto the ship - and still have another meal if you like.