As mentioned, cruise ships usually start boarding four to five hours before departure and won't allow you to board until they're ready. So there's no use in arriving at the cruise terminal first thing in the morning as you'll have to wait around for hours before you can even board.

While you can arrive at the cruise terminal earlier than your assigned embarkation time, it is generally discouraged and may result in you being asked to wait outside or in a secondary holding area. Cruise lines use staggered arrival windows to prevent overcrowding and ensure a smooth flow of passengers. If you arrive early, the staff may be busy helping the previous voyage's passengers disembark, and the terminal may not have the capacity to seat you. The only travelers who should arrive at "any time" are those with Priority Boarding perks, such as suite guests or top-tier loyalty members (e.g., Carnival's "Faster to the Fun" or Royal Caribbean's "The Key"). For everyone else, arriving exactly at your scheduled time is the best way to minimize wait times. If you have a long gap between your flight and boarding, it is better to drop your luggage at the porters (who are usually there starting at 10 AM) and explore the port city for an hour or two.