Echo amyg above: When DH and I went last year, staying on Harbor Blvd, we'd get to the gates 30-45 minutes before opening. I'd put in a Starbucks order on the mobile app, and he'd go back through security on the DTD side and pick it up. He'd leave his bag with me so getting back through bag check was faster. Then we'd have coffee and breakfast sandwiches while waiting at the turnstiles. I will say, though, that he almost didn't make it back to the turnstiles one time; had about 3 minutes to spare before they opened.
Also, I'm a fan of having stuff on hand in the hotel room, assuming you have a mini fridge, as most places do. Yogurt, fruit, granola bar, enough to hold us over till an early lunch, with a Dole whip or something delicious in between.