For the trails that DO have quotas, and that show online that they are fully booked, the noshow permits become available at 11 AM for same-day starts.

And ALL the trails with full quotas, except the Mt Whitney permits (both day use and overnight), 40% of the slots are held back for NEXT-day entry, and they become available at 11 AM also.

So not much sense getting there when the permit office opens, if you want one of those.