Omega should become available at the same time as Early Access to Stormblood starts, i.e. on June 16th after maintenance ends.

"Because we anticipate heavy server load due to the start of early access and the implementation of Patch 4.0, the World Transfer Service is scheduled to be available again on Jun. 16, 2017 at around 12:00 (GMT) / Jun 16, 2017 at around 13:00 (BST)."
http://eu.finalfantasyxiv.com/lodest...d8a0a50457be46