Air bags could lift it, but then you have the problem of dragging it out and rupturing the bags... a crane can't reach it with the roof intact.
There is probably not enough headroom to snake a knuckleboom crane inside and lift... I wonder if they will have to break the front wall and excavate a ramp- or just build a new floor over the carcass?
Minor personal note- I did extract a car from an abandoned septic tank it fell into, years ago. The owner did not know it was there ( city sewer service had been available for years, the tank predated that. )-- but it was dried out, and only the front end was "down by the head"-- not the whole car.
It was a simple "J-Hook the axle and winch" operation.
BTW- note the rough, dark rectangle in the back wall? It almost looks like a doorway- wonder what purpose it served.
It's a simple matter for a mobile crane, though they may have to take off the garage door and punch a hole in the front over the door to allow room for the boom. Build a support frame under the car, attach cables to all four corners of the frame, drop the crane to minimum altitude over the Escape, reel/lift the frame up, drive the crane out or collapse the boom, bringing the car out of the garage.
This may have been an old 60's bomb shelter from the cold war era. I can't see a sistern being there..........