When you are about to enter the armory, on the right side of the big steel door that shuts permanently, crouch and you can fall through the floor into the armory without setting off the clock timer.

But do not go anywhere near wher the elevator lowerest, as this completes the loot part of the mission, and you cannot get back in unless you are teamed with a player who has not done the quest yet (that last part is from personal experience, my Berzerker is currently locked out).