In season 2 the episode Journey to Babel, we find out that Spock entered the academy 18 yrs prior as was already stated by Nerys Myk. If the academy is a 4 yr program and you typically start at age 18, then Spock was 22 when he graduated and at age 36 when JTB happens. In the Deadly Years which was in Season 2 Kirk States he is 34. One could assume that in the episode Menagerie in season one, Kirk was 33. Per Memory Alpha under the episode synopsis, the events of the episode The Cage and the Enterprise heading to Talos occured 13 yrs prior. That would mean that Kirk was 20 yrs old during the events of The Cage. Kirk would probably still be in the Academy for another yr or 2. That would also mean that The Cage was one of Spock's first missions. It's not "unreasonable" to think because he is a Vulcan with a nice intellect that he got a post as Science Officer for the Enterprise as his first assignment. But there is also a window for Kirk to be a sophmore while Spock was a senior at the academy. It could be plausible that as Spocks last commitment to the Academy as a Senior before going on his first mission was to try and bust this wunderkind of a phenom sophmore human known as Jim Kirk as nothing more than a cheat concerning the Kobyashi Maru. Probably because no one else has ever done it and its the logical thing to do. However Kirk does not get in trouble for cheating, infact he gets rewarded, because of this he likes Spock nonetheless, he understands Spock's use of logic. Besides, no one would find out he cheated if Spock doesn't bust him. Spock then goes to the Enterprise under Pike while Kirk finishes school. Because he's Jim Kirk and the coolest badass ever and he beat the no win scenario he obviously rises to Captain alot quicker than anyone else after graduating and then serving in various positions. When Kirk gets the news he's in command of the Enterprise and is aware that Spock is on board as Science Officer he requests that Spock become first officer. Spock has 13 yrs on the ship and is familiar with it, he knows some of the crew,and because of the Kobyashi Maru, Kirk knows Spock will always do the right thing even it means going against the Captain. This is just how I picture it. But it does make it feasible for them to be at the academy together. I also imagine that Scotty, Uhura, and Sulu were already serving on the Enterprise under Pike before Kirk, for just a few years at best. If Kirk was 34 and Spock 36 in season 2, I also imagine McCoy being around 40, that puts him at 39 in season 1 and 66 in TUC when he says he has been chief medical officer for 27 years at the trial. In Generations it states that it is 78 years later so if we minus 7 yrs from the show to put us in Season 1 of TNG that leaves us with 71 years and if we add that to McCoy's age of 66 in TUC, that Makes McCoy 137 yrs old in Encounter at Farpoint. I think they state his age as different by a year or 2 but it is close enough for me. It's kinda sketchy but that is how i rationalized it. I don't think Kirk and Spock were friends at the Academy. They knew of each other and had a rivarly as any underclassmen would have with a Senior. Why does that stupid movie Drumline come to mind? Anyhow this rivarly created a working relationship that developed into a wonderful friendship as well. In my experience some of my greatest competition have become my greatest allies. But to answer the original question for this thread, until the news of this new movie, I just assumed they met when Kirk took command in WNMHGB.