Throughout April, as lottery winners log in and decline slots they can't use, those show up as available at a random time within 24 hours after they cancel their slots.
On May 1, the unclaimed slots -- those won, but not paid for by the winners -- are made available. (I am not sure, but I think those become available at various times through the day.)
skylerd: They don't make them immediately available at a specific time, and not immediately after someone cancels, to prevent scalpers from picking up permits, and then coordinating with someone to grab slots as soon as they are cancelled.
Best thing to do is set up a link that you can "bookmark" that hits recreation.gov for the specific dates you want to see, for the specific type (day use or overnight), and keep checking for anything coming available.