Aside from ZOS maintenance lasting however long on early access launch day May 20, early access starts whenever that gets done - presumably ~afternoon'ish PDT time.
But noticed on my Steam pre-purchase of Elswyr upgrade that on purchase confirmation screen it stated 'available 5/21" - assuming this isn't a typo or mistake, that means absolute best case if this steam availability notice is correct is 1 minute after midnight on 5/21, or about most of a day to half a day depending when maintenance ends and Steam users can start playing.
Note - I'm not talking about the Steam store date which still says June 4 - I am talking about when you -actually- buy the pre-order, the confirmation of payment, etc screen shows the notice 'Available 5/21'.