We're going in early June and with the opening of Pandora, I was sure to be up and ready at 7AM EST (5AM in Colorado where I am). Got everything we wanted, finished booking 6 days of FP's in about 25 minutes.
That being said, out of curiosity, I logged back in a few hours later and then that evening and then in the following days at random hours and was surprised that almost everything I wanted was still available, even if off by a little bit of time - say up to 2 hours).
Here's my advice: If getting up at 7AM and being ready to go (or 4AM if you're west coast) will calm your nerves and feed the excitement as it does for me, do it. But if you're a few hours later, you're still going to be able to get what you want within a reasonable time frame. Wish I hadn't stressed that there wouldn't be FoP, 7DMT, Frozen even while I was logging in. But the thrill factor of getting to literally cherry pick FP times - that's worth getting up for in my house.