Great post Sci! 
To clarify one statement:
You're right, insofar as what is in the theatrical release. But I believe someone mentioned that in the deleted scenes (and in the novelization, based off an earlier script), the scene prior to James stealing the car is James washing the car. It is at that point at which we are informed that the car was originally his father's car, and in fact James is cleaning it because his step-dad intends to sell it.
And to just throw in my opinion on another point:
Like the majority of posters, I too agree that this was purely a conceit for us to have the "reward" at the end of the movie of seeing Kirk in his gold command uniform as Captain, and it could have been done other ways that would have made more sense.
However, if we accept (and I do) that Kirk, like the other pre-graduate cadets, was a lieutenant, he was only promoted a couple of ranks, not across the entire rank structure. Also, I'm going to guess (just my hunch) that not every officer cadet takes the Kobiashi Maru test, that it is specifically taken by cadets aiming to become captains of starships. These two details already suggest that Kirk is a lieutenant cadet who leadership understands (and perhaps is even grooming) to be on the path to Captain.
Add to this the fact that Pike is not simply an Admiral now, but one who had been in charge of recruiting, had probably overseen Kirk's career, had a massive soft spot for him, and of course owes him his life. It is not much of a stretch to imagine that Pike could have pushed very hard for Kirk to relieve Pike, using both his rank, his familiarity with Kirk and desire for more "leap before you look" Captains, and perhaps even playing the "sympathy card" of his injury to pull favors.
None of this is to suggest that it would have been likely or smart to promote a rather reckless Lieutenant with limited command experience, even if he did save earth and rescue an officer from imminent death. But there are enough threads of why it might have happened that I can enjoy it as it was.

To clarify one statement:
George Kirk basically restored a museum piece, a 20th century car.
Sci said:Actually, dialogue seems to imply that the car belonged to the unseen adult male that Kirk's mother was living with (presumably Kirk's step-father). There's no evidence that it was the property of Kirk's father George.
You're right, insofar as what is in the theatrical release. But I believe someone mentioned that in the deleted scenes (and in the novelization, based off an earlier script), the scene prior to James stealing the car is James washing the car. It is at that point at which we are informed that the car was originally his father's car, and in fact James is cleaning it because his step-dad intends to sell it.
And to just throw in my opinion on another point:
If JJ wanted Kirk to be the captain at the end of the film, why the hell didn't they do a flash-forward? "Three years later" or something like that.
Sci said:Very strongly agreed. The insta-promotion was stupid.
Like the majority of posters, I too agree that this was purely a conceit for us to have the "reward" at the end of the movie of seeing Kirk in his gold command uniform as Captain, and it could have been done other ways that would have made more sense.
However, if we accept (and I do) that Kirk, like the other pre-graduate cadets, was a lieutenant, he was only promoted a couple of ranks, not across the entire rank structure. Also, I'm going to guess (just my hunch) that not every officer cadet takes the Kobiashi Maru test, that it is specifically taken by cadets aiming to become captains of starships. These two details already suggest that Kirk is a lieutenant cadet who leadership understands (and perhaps is even grooming) to be on the path to Captain.
Add to this the fact that Pike is not simply an Admiral now, but one who had been in charge of recruiting, had probably overseen Kirk's career, had a massive soft spot for him, and of course owes him his life. It is not much of a stretch to imagine that Pike could have pushed very hard for Kirk to relieve Pike, using both his rank, his familiarity with Kirk and desire for more "leap before you look" Captains, and perhaps even playing the "sympathy card" of his injury to pull favors.
None of this is to suggest that it would have been likely or smart to promote a rather reckless Lieutenant with limited command experience, even if he did save earth and rescue an officer from imminent death. But there are enough threads of why it might have happened that I can enjoy it as it was.