The computers roll forward to the new day sometime between 6-7am. So you should be able to "check in" sometime after 7am.
As to when you will get your room, that's a different matter. It depends upon occupancy the night before, number of rooms to be cleaned, etc.
Our record was 8:30am at OKW. That was a Sunday arrival (room was clearly empty from the Saturday night before.) By 9am I was enjoying the view on the balcony.
But realistically you need to plan as if you won't get into the room until after 4pm. How early you arrive may or may not have any bearing on when you gain access to a room.
The last time we went to Disney was in June and we were in our room by 10:30. Room was ready when we checked in at SSR. We have also had to wait close to 4 before at OKW because we wanted to be close to the HH.
Landed at Orlando at 6 am, magic express dropped us at OKW at about 7, we were in room at 7:30, had breakfast at Boma at 9:30, we were a half hour late. Had trouble leaving the room.
We got into a 1 bedroom at OKW at 9 AM on a Sunday once...we were thrilled! I was also able to get a dedicated 2 bedroom at VWL on a Sunday once before 9. I had been in a studio the night before and just thought I'd ask. That was great...got the shopping done and food put away before the rest of the family got there!