Let's look at an optimized Artist. Great Dexterity (x2), Affinity with Craft, Puissant Craft, Inspirational, Free Expression, Artistic Renown x2. Most starting characters have a maximum Ability cap of 5, and let's assume Artes Liberales 3 as well. This starting character has spent 8 points on virtues (room for 4 more) and produces an AQ of Craft5 + Specialization1 + Dexterity5 + Puissant2 + Inspirational3 + Free Expression3 + ArtesLiberales1 = 22.
Now, here's the bad news: AQ22 takes 3 times as long to make anything, so it's not 1 Reputation per season, it's 1 per 3 seasons. If we start out artist out at Age20 with a Reputation of 4, meaning he needs 25xp to get to Reputation 5. Let's assume that the character spends 3 seasons making Art and 1 season finding a Benefactor - each time he gains a benefactor he gets +3xp to Reputation (Benefactors are better than Patrons, as you get +3 each time you find one and suffer no losses from losing them). So the Artist is getting 4xp in Reputation each year.
His Craft will advance 3xp/season (Affinity on Exposure XP) - let's assume regular xp from the free season go elsewhere.
After 8 years of work the Artist has gained +2 craft skill (Craft7/147xp) (+2xp Rep) and +32xp Rep from working, so he's at Reputation 5/84xp
After another 8 years the Artist has Craft8/219xp (+1xp Rep) and another +32xp Rep from working, so Reputation 6/117xp.
After another 6 years the Artist has Craft9/264xp (+1xp Rep) and another +24xp Rep from working, so Reputation 7/141xp. The artist attracts a lesser Muse at this point (3xp Reputation, now 7/144). The Artist is 42 years old at this point. Let's assume the minor muse infuses 5 Might into the artist. His AQ is now 27.
Getting to Reputation 8 now requires another 36xp in reputation. Let's add 8 more years (+32xp rep) and acquire a Patron (+3 more rep over a Benefactor). The artist is also at Craft11/336xp (+2xp rep), so at age 50 the Artist has Reputation 8/181xp. His AQ has jumped to 29 (still only triple time).
Now things get worse. The Artist has a Patron, so he's only getting Reputation from making art or from fantastical stuff (studying under magical beings, adventure, etc) and he probably slows down to 2xp/year at most. He still needs 149xp to reach Reputation 11/330xp, and he probably won't live for another 75 years (125!) to manage it (maybe if you have a Supernatural Virtue and a Longevity Ritual).
Realistically, the only way to manage it is to pursue the special means of gaining Reputation. Study under a Might 30 creature for a long period (6xp rep a season) is probably the fastest way - if you can find and study under a Legendary Artist, they are sure to be at least Might 26-30 (Craft 13-15) and provide 5-6 Rep xp/season, as well as being able to teach to a high level of Ability. Note that the Reputation system REQUIRES you to have a Patron in support of you beyond a certain point (8) and this immediately strangles your ability to gain Reputation XP, because your patron wants you working or they abandon you and you lose a ton of XP (this is ill defined considering characters are assumed to have 2 free seasons a year).
A PC patron solves that issue. So you need a really tolerant patron and probably need to study under an existing Legendary Artist or other magical beings to stand a chance. I'm sure the numbers can be juggled better - you can start with a lower AQ (11-20) until you hit Reputation 6 so you gain Reputation xp from work faster, but then you struggle to hit later AQ requirements to gain Reputation xp - it's easier to front load the virtues.
Artist Reputation is mostly to allow them to find Benefactors so they can cover living expenses.
EDIT: Note once the artist hits Reputation 10 they can freely experiment without the possible reputation hit, which can get the artist a rep bump fast if he's lucky, but he's still in the 95 year age range under 'normal' progression.