Try to hit the submit button on June 1st or 2nd or whenever it is AADSAS opens up. Even if you haven't taken your DAT score yet, still apply that early because as people mentioned before, LOR's grades etc take a long time to update. You DAT score will upload like two-ish weeks after taking it, and from there schools will have everything and start to review you. Ideally, you'd already have your DAT done by June but if you don't that doesn't mean you shouldn't still apply early.