You definitely want to try booking them an hour before midnight of the day you can book.
The reason I say that is that I did see a report that said someone was able to start their booking that early. Keep in mind however that
MDE and the Fast pass site is GLITCHY so it's like Forrest Gump's box of chocolates... you never know what you are going to get as far as when the site will work correctly.
When I booked 60 days prior to my upcoming trip the site did not start working to accept Fast Pass bookings until 1 am... so it can be all over the place.
Also do not expect to change your ROOM only reservation OR Resort PACKAGE booking and expect to keep all of your previously booked fast passes. Even booking a dining plan AFTER YOU HAVE MADE FP SELECTIONS
can wipe them out because your hotel reservation changes.
It's best to get your ducks in order and commit to your hotel/dining/resort package type AND THEN BOOK YOUR Fast Passes. Once Disney Wipes your FP because of a reservation change there is no retrieving them... they are gone forever, just like Olaf on a warm summer's day. You have only the memories of them and the angst of trying to book them all over again...
~NM