That hatch should be larger than the opening and never fit through it unless rotated 90 degrees horizontally and again sideways.
This is an almost full size exit door, not an overwing exit. It is too big and heavy to do what you propose.
When used as an emergency exit door, it was designed to move up out of alignment with 12 stops that hold the door in against cabin pressure, then once clear of the stops it rotates out and down on two hinges at the bottom of the door, also activating an emergency slide.
The plug that departed this aircraft is used when the emergency exit is not needed (due to max passenger capacity configuration) and mounts just like the emergency exit door, but is supposed to be bolted in so it cannot move up out of alignment with the door stops.
The door plug was removed to rework some rivets next to the opening, and when Boeing workers reinstalled the door plug they never reinstalled the retaining bolts the permanently lock the plug in place, which allowed to door plug to eventually work its way up along the tracks and then pop out.
This took months and several flights. The plug is covered with a standard inner wall panel, so you cannot even see the door plug from the inside of the aircraft.