Go to the first trivia game, there will be several. You can join a team or play alone, but you will soon have some familiar faces as you go around the ship. They often have team games too, so join up. Take a class if something is of interest.
It doesn 't feel awkward at all, I go to bars,and shows alone, things I wouldn't do at home, but it's a cozy feeling on board, you won't feel out of place.
You only have yourself to please, so do anything you want!