I'm pretty sure you can use the Parardise Pier entrance which is just to the right of GCH front doors down the path.
There is a wrought iron gate that you have to use your room key to get into. I assumed all Disney resort keys would work, not just PP. We were staying at PP, but when we got to the gate at 9:45 for a 10:00 open, there were alot of folks and they already had used a key to open the gate...draw your own conclusions!
It is SUPER first thing in the morning if you want to start on that end of the park. Takes a while for everyone else to get there from the front. You can ride Screamin 5 times with no wait - if you can stomach it!