Ok so you won’t ever get an empty park. It just unfortunately won’t happen.
Now there are some times of the year that are really busy. By 10/11am the crowds are every where. One of those times just happened-the Christmas/New Year holiday season.
Now I cannot stand it when Disney World is really crowded, and I try to avoid all times super packed. But with family visiting they wanted to go on some of the busiest days-so we made a plan to avoid as much of the crazy crowds as we could.
Book a breakfast inside a park before the park opens for the day. Try to pick a day with no Extra Magic Hours. This way the only guests in the park will be those dining. We did this with Disney Junior Dine N Play Breakfast. We had an 8am breakfast.
I loved being able to capture this shot of no one in the background.
Once breakfast is done head over to the rides/attractions that will get the longest lines fast. At Hollywood Studios we had fastpasses for Toy Story Mania so we ran over to Rock n Roller Coaster.
Some parks are less busy at night. One evening we headed to Animal Kingdom at 7pm. It was open till 10pm.
While Flight of Passage and Navi River had excessively long waits, all other rides/attractions were reasonable. We were practically the only ones on Kilimanjaro Safari.
Most days we would leave the parks by 11am/noon, and had gotten in a good amount of rides and attractions.
And we had the added bonus of many pictures with no one in the background!