On an EMH morning a week ago (last Thursday) we were walking up to the bag check just as the opening show was ending, .. and even though we didn't sprint to any rides, we were able to get on 4-5 rides before our 9:30 AM fast pass (that was still so early it wasn't even needed).
I decided to hit Tomorrowland first .. so we hit Buzz twice, Tomorrowland Speedway, TeaCups several times and Little Mermaid.
There was plenty of time for a leisurely stroll up Main Street .. some Photo Pass photos and those rides and a bathroom break all before 9:30 AM when we headed over to Enchanted Tales with Belle.
If I didn't have a toddler with me (who dictated some of the ride choices), we probably could have hit Space Mountain or any other Tomorrowland attractions if we wanted.
I would hit some of the typically longer lines first:
Space Mountain
Peter Pan ..
Tomorrowland Speedway (if that interests your family)
Haunted mansion (on your way to BTMRR after normal park opening)
Heck .. maybe even just beeline towards Seven Dwarves Mine Train to go on it twice that day.