Even if you do not have EE I suggest showing up a little early by getting through the gate and hanging out in the holding area until they let people in. Even with no EE, they usually let people in a little bit earlier than 9 (about 10-15 minutes) so that might help a little more.
As others said it depends on what time of the year it is, but even if it's busy, or moderately crowded, the first hour for the most part is walk on, or low wait times. However, last time I went it was a 90 minute wait already for Gringott's (and it was during EE), however during the day it would be a 45, 55, or 70 minute wait. So, if something seems a little too much for you, I recommend you to move on, and hope to catch it later, except Minions, that ride never seems to go down (probably because it's for the kids). So, depending on where you go, how close all the rides are that you want to enjoy, how well you plan, you can get a decent amount of rides in before 12.
Also, single riders can be your best friend, especially early in the morning if you do not mind splitting up with your party and don't mind meeting each other at the end of the ride. Sometimes when there is a crazy wait time (or later in the afternoon), there might be a lot of people in single rider, and the wait can be unpredictable and long. However, if you do single riders, especially in the morning, everything will definitely be walk on (that's what I do a lot).