Excellent responses, I have to say.
For my money - the key to quickly gaining power is to find and maximally utilize high-Quality sources on a few (ideally two) Arts. You'll also want to invest seasons into making a familiar and perhaps initiating Mysteries and so on, and of course for learning spells etc; but that's on the side. The main point is to raise those Art scores as high as possible as quickly as possible.
You should choose one method of advancement and optimize it. Select Virtues and arrange in-game circumstances to maximally exploit it. While books are the obvious choice, I think studying raw vis is actually superior in most sagas. (It depends on raw vis and aura availability, compared to book availability.) Assuming an aura of 10 is available, average Quality is about 16. Realms of Power: Magic offers variants of auras that might even be superior, but I don't remember the mechanics; either Aligned auras or auras within the Magic Realm itself may provide a greater bonus, I think you can get as much as a +20 aura for Quality 26. Now pile on Affinity with Art (x1.5), Free Study (+3), and Study Bonus (+2); this brings you 31.5 XP on average on aura 10 or 46.5 XP/season in aura 20. I'd also get Secondary Insight for extra XP, especially if you can get some of your virtues to apply to increasing the effect (e.g. +3 from Free Study). You'll want to invest heavily in a good familiar Golden Cord, and if you can get your troupe to agree that studying in the lab allows you to apply Safety to the rolls then you'll also want to personalize your lab to increase its safety as per the Covenants rules.
Note that as a starting specialist you might get about 90 (post-Affinity) XP in the Art, and Art 40 requires 820 XP. So you need to gain about 730 XP to reach top-Hermetic power levels, which at 31.5 XP/season comes down to about 23 Seasons and at 46.5 XP/Season to about 16 Seasons. You probably won't get to do nothing but study so efficiently for 40-odd straight seasons (enough to raise the two Arts to 40), but finding the necessary time and resources within 20 to 40 years should be doable with an accommodating group, with time spare to invent spells, set up laboratories, and get into all sorts of adventures.
I would also strongly recommend aligning with the Infernal. Picking up Cthonic Magic is easy, and opens up using Infernal auras as well as applying a second Focus to your magic. The advantage of Infernal auras is they are very easy to build-up - using the RAW, you could fairly quickly and easily ratchet up an Infernal Aura of 10. Furthermore, using potent Infernal vis ("vis prava") can add bonuses to the study total for studying from it; as much as +8 by level 40! (i.e. +12 with Affinity), and as a side-benefit you also get +5 XP for using Corrupted Arts. Infernal magic comes with other benefits too, like the Forsaken duration. Granted, there are certain, ehm, side effects to such practices. But if you really want a power-boost, and can weather the storm, the Infernal can give you that extra push.
Cheers,
Yair