Think about the big box as a means to enter another quantum reality besides the physical reality that got you to the island. The only way to travel to the latter is the sub.
The producers have said that there is no "time travel" but chose their words very delicately here citing that time may "move differently" on the island.
I presented the unifying theory of lost with help of the wikipedia info, very complex, but it really is not. Deja Vu, the unexplained interaction of particles, the miracles of life may be due to the influence of similar quantum realities with our own. I nickname this quantum averaging, but to the onlooker, it would look like a betrayal of David Hume's constancy principle leading to the unexplained, the bizarre, and the unpredictable.....ie the island.