Go around the crates to the back left corner and pull the first movable crate out twice.
Climb over it to find the passageway leading to the switch that opens the exit. The door is on a timer, though, so you'll need to move a few crates out of the way to clear a path to the exit beforehand.
Push the crate you just moved once more from behind.
Then climb back over the crates to the area near the window.
Stand on the left side of the crate nearest the window (i.e., the left side when Lara's back is to the windows) and push it once.
Turn to the crate on the left and pull it once, so it's next to the last crate you moved.
Climb over it.
Then push it once more from behind. Now you should have a clear path through the room.
Now go to the end of the passage and pull the switch.
A brief cut scene shows the door opening. You can cancel it and get Lara's perspective back by tapping the Look button.
Then roll. . .
. . . run back along the passage and to the left. . .
. . . around to the right. . .
. . . and on through the door before it closes.
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