I agree -- the best time on the ship is just before the sun rises, literally watching the dawn of a new day. I enjoy time up on deck, with a cup of tea, while most passengers are still asleep.
I admit that I do set an alarm (I have a small, battery-operated travel alarm clock), as this is one aspect of the cruise I do not want to miss. There's plenty of time for a nap in a deck chair later in the day.