I've seen games and dlc go live anywhere from 6 am EST to around 10 or 11 (also EST) given that this is a bigger named game than others I would say it SHOULD come out earlier in the morning. Shame DLC doesn't come with "pre-order" options to leave the xbox online to download while we are asleep or at work.
Most of the time its been around 3 or 5am, though other things lately, the 'bigger' dlcs like story mission and content such as that you might be waiting until 8 or noon, or even have it pushed back a day further for being a xbox dlc or something silly like that. Patience is a virtue young Vault Hunter. All good updates come to the ones who wait. Just wait by grabbing a few more heads from Henry and snagging the color skins from the Hyperion assassins and threshers, or do a multiplayer session and help some one level up.