I'd push, or if it's just you, maybe get creative with ropes...find (or create) a secure anchor point on the wall, attach a rope to the car then while your in the driveway (with a little push) you could lower the car to you; for putting back, attach rope to other end of car, and attach your end to another car and pull the Box back to garage. Admittedly, the potential for catastrophic failure is high, but in theory, it should work. Still, I'd prefer to use muscle. As example, many years back I was at a party and a few of us thought it would be funny to move the car of the person throwing the party (as they had passed out); they had a two car garage, and we opted to place his car perpendicular to the garage walls...with about 4" of space at each end. We did this with about 6 people. I failed to mention this was a Super Bowl party and they had to be to work Monday morning, which to us (or the younger versions of us) made it even more hilarious. Strangely, we were never invited back.
Beer is a good idea, but maybe provide AFTER car is moved. As I've grown older, I've also gotten wiser...and in retrospect, the roof would have been far funnier.
EDIT: seriously though, I wouldn't start it. I had an impeller failure years back that I didn't catch for a bit and resulted in a system flush.