We have early arrivers (MUCH preferred over those late comer/stragglers!) nearly every Sunday. We use it as a time for the shepherds (who get there ten minutes early) to chat with the kids and review memory verses with them. For super early arrivers, I've had the kids help me set things up in the classroom.
We have a variety of books of the Bible activities - we have puzzles (make your own by spray painting the puzzle and box and using a paint pen to draw the verse, books, etc. on it), Bible book stix (write the books on craft sticks and have them put in order) or use cards. We also made Bible Book blocks as a project in our art room several years ago. They can put those in order, or categorize according to the types of books. It's prime time for memory verse work -- write out on cards and put the verse in order or write on an erase board and erase a word or two at a time.
You can also make out cards that correlate with the lesson -- I will often search for clip art that relates to the story. You can make a single card or duplicate so there are matches. Hide the cards around the classroom and have the kids search for them. Then find the matches (if you duplicated) or have the kids tell you how the cards relate to the story. You can use the cards later on in the lesson as a matching game. Can even have the kids "help" create the game by coloring in the cards for you.
Another thought is to use journals.You could add some simple art journaling to go along with their memory verse or a key word or phrase from the story. We are doing art journaling activities more and more with our kids and they love it!
Hope some of these ideas might help! What a great problem to have!