Once we had spent the night before in a value studio, and we were escorted right upstairs to check in and use the lounge. It was between 7 and 7:30 AM.
I believe it is 6 am when the resort 'turns over' and starts the new day, so you would be able to check in and have access to the 6th floor from that time forward, although I don't believe that breakfast starts, or the club level desk is open until 6:30 am (they desk may even open later than that). I know that we have checked in downstairs in the main lobby (I checked in while DH was storing our bags for the day) and then gone up to the lounge at the start of breakfast in the past, which would have been around 6:30 am.