The Port of Seattle doesn't advertise the time that the terminal opens to passengers anywhere that I can find. Although if the prior cruise is disembarking around 9:00 I would assume the building is open. It just depends how long you want to stand around waiting. There's really nothing to entertain you while you wait at the terminal.
While the building is open, it's really not a place that you want to sit around. It is nothing like the lovely terminal that Disney has built in Port Canaveral. It's basically a warehouse that you walk and wait in line through. Out front there is a coffee stand, but that's it.
You really don't want to aim to get there until after 10:00, prior to that it's going to feel chaotic because of the passengers who are leaving from the previous cruise. You will be like a salmon swimming upstream. Whenever I disembark in Seattle, I make sure to be in the last group of people since I'm not trying to get to a plane, and the foot traffic is still heavy.
If I may suggest, since you're awake anyway...The Olympic Sculpture park is on Western Ave, about a third of the way from Pike Place to the Pier. it's free, it's art, it's got the best view in Seattle. You'll be able to see the Wonder from it. If you have kids, it's a great place to run around. If you're an adult, it's a great place to take a stroll with a cup of coffee. http://www.seattleartmuseum.org/visit/OSP/default.asp#parking
Or go to Pike Place, some coffee and cafes and vendors open at 7am, with the rest (except for DownUnder) opening at 9am.
I think you're probably going to get the same answer from everyone who's been to this pier... even if you could get in earlier, you wouldn't want to. Even if you were flying in that morning at 7am, I'd recommend staying at the airport rather than heading early to the pier. At least at the airport there is some decent food, art, and stores. And yes, I know how funny that sounds.