Q: If you are trapped inside a box...

If you are trapped inside of a box, inside of another box, which was surrounded by thousands of other boxes, and every time you tried to escape, more boxes would form and you would get trapped even deeper in the sea of boxes, how would you get out? - LMAO

A few ways:

Prevention:
I'd make sure not to get caught in the first box in the first place

Reverse Approach:
You said that every time I tried to escape more boxes would form, but that would be me working from inside-out. I'd sit still and have call someone on the outside break through the boxes from the outside-in.

Shovel:
I'd dig underneath the boxes and tunnel to safety. The ignorant boxes would think I was still inside them. Once a safe distance away I'd commission a helicopter, fly above the boxes, and firebomb them all.

Philosophical Approach:
If you consider my apartment to be a box, Earth to be another box, the solar system to be another box, etc. then I could live my entire life in the scenario you described, so it would be fine by me not even to try to escape.

Self-Destruct:
Since I wouldn't have long to live anyway, I'd set myself on fire. It'd be painful but at least I'd take all those boxes with me.

Space
I'd make a call and ask that me and all the boxes be launched into space. While floating in space, I'd keep trying to escape, causing more and more boxes to form around me. Eventually the box would grow so large that we'd reach a black hole and me and all the boxes would get sucked inside. In the black hole's parallel universe there'd be one box inside me and everytime it tried to escape another Adam would form to contain it. @_@

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