I was there July 10-14 and at US, they let us in as early as 8:30 one day. Rides were running too. At IOA, it was around 8:45. I think it varies from day to day, but I'd be there at 8:30 to make the most of the time just in case.
It can take 15-20 minutes from the parking garage. Use the moving sidewalks when possible. In the morning people seem to walk on them but in the afternoon they stand still.
It is pretty common for the parks to open 15 minutes early. When its busier they open earlier.