I tend to start PCs at level 5, because I wanted the option of a Harry Potter-esque adventure where young'uns learn magic slowly. I mean, Harry's just 14, and he can cast pretty impressive spells, it seems (Patronus would be, what, summon monster 3 at least?).
Anyway, I realized that core D&D advancement are silly and too fast when I proposed this idea.
Two rivals at a dueling school are both 1st level Fighters. Every day they fight each other with padded weapons, hoping to defeat the other. We'll assume they're pretty evenly-matched, so they'll each win half the time. Since the damage being dealt is subdual, they'll heal up quickly enough to fight against the next day.
So, after 8 days, each of them has won 4 times, defeating 4 CR 1 encounters, each worth 300 XP. Each has thus earned 1200 XP, making them both 2nd level.
6 days later, with 3 more wins each (1800 XP more), they'll both be 3rd level.
8 days after that, they're 4th level.
Every few days they change up they're duels. Sometimes they fight blind-folded, sometimes with their off-hand, sometimes on dangerous precipices, or with different terrain, in harsh weather, at night, with different weapons, etc. This way their training covers
I think we figured out that 140 days of daily training, these two fighters would both be 20th level. Sure, they wouldn't have any magic items from adventuring, but they have tons of experience fighting. Even if we use the General Downtime variant option in the DMG, where you have to spend 1d4 days per level resting whenever you level up, that's still merely an average of 525 more days. So after 665 days of training and study, not even two years worth of time, you have 20th level fighters. Sound a little fast to you?