I don't think it's that early. I think it's like an hr before park opening, and if it's EMH early day, say, 8 am EMH for a normal 9am day, GR would also open at 8am. Depending on how late, it might be an option to either go to a late hrs park like MK or go to a Disney Springs ticket booth. Disney Springs is open later typically, and the ticket booths have about the same capabilities as GR at the parks. For RotR, we were getting there by 6:30 for 8/9am on 12/5-12/6, and boarding groups were already 40 and 25 for those days. Not sure how they are post grand opening, but probably not significantly easier yet.
So the past 2 trips, we flew the red eye and took the bus over to hotel after midnight. The 1st trip being in Aug., there were room availability and they let us in early to nap before 1st park. This past trip being on Thanksgiving Day- they were actually overbooked according to CM. We felt like hobos, but we sprawled out on the couches in the lobby in front of the TV. Every time I saw people checking out, I asked for a room, and finally was able to get one. And we were able to grab a nap and store all our luggage. It was tempting to go to HS (open at 7, no RotR yet but we haven't been on Smuggler's), but we ended up going to AK (9am) so we could RD what we thought would be the least busy park that day.