Costuming has early shifts too. (They also have some pretty late ones.) I had shifts start as early as 5:30am, but most of my early shifts started at 6 or 7am. I ended up with those a few times a month & when I did, I usually had 2 or 3 of them in a row.
If you don't have a car, early shift suck. The busses don't really start getting to the parks & resorts till after 6, so I always had to call for an early pick up at 5, but since I lived at Chatham & the 5am run was only from Vista, I had to take the 4:35 mk bus to vista, just so I could get to work on time.