We were the first group off 8am way back in 2011 so use this as a rough guide since I'm sure the logistics of this excursion probably have changed.
Plus if you are an early excursion, things tend to run very quickly before the crowds emerge.
8:00-8:05 walked off the ship / thru customs / boarded shuttle bus. (really fast and efficient. we were one of the first groups off)
8:20 - dropped off at front entrance of Atlantis
8:20-8:40 - not knowing what we were doing, we stupidly waited with the group at the entrance for a guide to walk us over to Aquaventure. They took us thru the entire resort - casino;shopping; etc.. and finally outside past the Dig and half way around the pool area.
(I'm not sure if they still do this and didn't realize you can easily just breakaway and go straight to Aquaventure since we already had wristbands on from
DCL.)
So that felt like a complete waste of time and the walk was pretty long. I kept thinking there must be a shortcut, but we had no idea where we were going.
By 8:50 am we found a great cushioned lounge area with umbrellas and small tables and settled in before the crowds arrived.
This was the last week in May. Not unbearably packed at all. We rode the slides and lazy river / walked over to the beach area to grab lunch around 11 / toured the Dig and hung out for about half the day. We were back at 1:30 believe it or not, mainly because I had my parents in tow who are in their 70's. But it was a great day and I could have easily stayed longer.