We come to a scene of a child and a mother at the doctors office receiving the news of what the child's quirk is. The doctor says "Ms. Midoriya it seems little Izuku here has a weak mental quirk that allows him to have a mental library of books he memorized."
"So I can't be a hero?" Izuku says tearing up while his mom starts hugging him while saying thank you to the doctor.
Like in canon Izuku has become quite depressed about not having a quirk that would let him become a hero so when they got home and Izuku was watching videos of all might, instead of being interrupted while watching the video he was tired because of having a quirk testing section, he fell asleep on the chair resulting in his mom moving him to his bed.
While in his sleep Izuku's mind moved into his mental library where because of the stimulation of his emotions his quirk and it's unexplored abilities the quirk was evolved to mage's library giving him all the books to become the best mage ever existed. As the library was a creation of the universe itself it has the best ways to become a powerful mage in any subject and path.
Izuku becomes aware he is in his mental library and sees countless books he never saw before so he gets out of his sadness as his curiosity has his mind ignoring everything and he starts walking toward a pedestal that was his height and was in a spotlight like area specifically grabbing his attention before he tries to explore the books in the library.
Walking up to the book on the pedestal he found it titled "The Library's Guide" opening it Izuku read that the library has the abilities to record books Izuku has read and keep them in a separate area from the new magic section. There is a magic section with everything one needs to know to become a mage in any path one wants examples like Elemental Mage, Psychic Mage, Non-Elemental Mage and many other paths. (Let me know what other mage type you would want to see I might be able to come up with new ideas for magics and rituals)
The library has the function of setting up an order for what the owner's desired path wants. Example he wants to become a fire mage the library would create a line of books of what he needs to know in order to be a qualified fire mage in the library's image. Or specifically wants to learn a spell like fire ball the library will set up a line a books on what he needs to know like the spell and what he should know in order to effortlessly cast the spell as the library will give him all the needed information to be the greatest at anything as long as he reads to the end of the line of books.
Izuku read through the guide then understands that this is his chance to become a great hero by being a great mage so he spends his dream learning about different mages and their abilities and rankings. He learned mages have two ways to rank them, by their heart circles and their body refinement 1 circle beginner and and first refinement enhanced body and strengthened composition. (Tougher skin and denser bones the muscles get stronger while still being the same size)
1-3 Beginner Mage with not much energy (Doesn't mean not strong just not a lot of mana so spell have to be weaken on purpose to not lose too much mana on each casual spell)
4-6 Advanced Mage more energy can use stronger spells and regen mana faster (Spells get stronger the more mana put into it and how well one understands the essence of the spell)
7-9 Master Mage can use hundreds of full powered spells and can regen mana to be able to cast 5th circle spells for a straight day before the regen can no longer keep up as it just barely uses more energy than their mana comes back
1st refinement body is strengthened to triple the base bodies abilities
2nd refinement body is strengthened to peak of the species abilities ex: Super Soldier Serum of Marvel
3rd refinement body has surpassed the limit of the species and will start giving abilities depending on the resources used to refine the body (To refine the body resources are needed) (Izuku will have to cultivate most resources on his own as his world has no mana to naturally produce magical ingredients and animals)
4th refinement body will start using mana to supplement itself and no waste is created ex: no longer need food or air and doesn't need to wash or poop as there is no sweat being produced unless controlled to let body sweat (Owner can control his body to such degree that sweat is optionable but lets be real at this point no one in MHA would make this body sweat at all so I'm going to stop here but there are higher refinements I just don't think it's necessary to include this as Izuku wouldn't need to go further into this as beyond this is just immortality from age and Izuku would have to have someone with him before going through with this refinement as he would then stop being human and moves to being a new species if he had a child during the fourth refinement the child couldn't be considered human and the mother would die if not strong enough to handle to baby pushing in her womb.)
After he read this rankings of mages he found his mind slowly falling into real sleep ending his first visit into his library.
*End*