ILL you should have your choice of times throughout the day.
I was staying offsite and bought ILLs twice at 8:30 (opening time for Epcot), with my choice of times starting at 2:30 or so. So if you are getting it at 7:00, you'll have lots of options.
I recommend trying to nab a VQ spot first, since those go much quicker than the ILLs, and they are free. Ride it twice, it's amazing!