From what you are telling me it sounds like you could have the main character get all the training but only hit the high points for the reader. Look at how JK Rowling handled what in some respects is very similar to what you are doing. Obviously there are differences but you have a person with no knowledge of magic suddenly finding that they are part of a magical society and having to learn the ropes. Of course in her stories the training is the story where it sounds like you just want the training to be the beginning of the story. Give the introduction or overview of the training plus two or three interesting anecdotes about the training to give the reader a feel for what's going on. The anecdotes will also give you an opportunity for some sleight of hand as you give some specific information while seeming to just give an example of the life of a mage in training.
This is not the only way to tell this. Much can be learned by conversation among people in the book. If you do this be sure to avoid talking heads unless you can, like Jim with Bob, turn the trope on its head and have fun with it. You can do some of it in flashback. You can have the main character find some of the information on his or her own. (Reading an old book or scroll, etc.) You can use any combination of these things.