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Siterus
If I was writing a fantasy novel with an orphan in need of money then I'd set out to have him do it himself in a cool way. (NO LUCKY COINCIDENCES! THAT'S BAD WRITING!)
1. Pickpocket. A staple of orphans and fun to read.
2. Thieves guild. Perhaps he's not a member. But he knows a guy that offloads some of the easier work to him or a specific task for a job he's pulling to him.
3. Scamming.

Now the above assume your MC is either a bad guy or in the morally gray area. If your character is Lord of the innocents then it becomes a bit more difficult. Especially since we know nothing about your MC. Still, here's a few ideas.
1. A skill. Perhaps he has some oddly specific niche he uses to ilk out a small living. Hunt rabbits and skins them? Or knows how to perform minor repairs for weapons and armor.
2. A job. It's normal for orphans to have jobs in a fantasy novel. He could work in a kitchen as the help. Do odd jobs around town.
3. He can switch his car insurance to GEICO. With his 15% savings, he'll have tons of money to spend on whatever he needs!

Ponzi Scheme

how much money? Simple - artisans apprentice.

again cheats... God, nooooooooo! Boring.
Politics, laws, economy, society. What can do a 10-13 years old character? Who does he know? Have a connection?
If need books - the road to the bookstore and work there. If books are rare - temples, monasteries. It is difficult to advise something when known nothing about the world.

1.Kills a bandit with a high bounty then claim the reward at adventurer's guild.
2. Save a beauty who is "accidentally" a noble then reward him with money.
3. Collecting herbs and learn alchemy and make/sell potion at auction.

Siterus if he can learn things very quickly how about letting him steal a letter, which actually contains a private information of a merchant. he saved the merchant by finding that letter and in return the merchant teaches him counting/ accounting and he shows his talent and in a short time finding profit for him and the merchant. maybe you can make him fall out with the merchant later on

haha lol... i wrote things usually used by reincarnated mcs, thinking that your story is also a reincarnation type....
well for stories with a fantasy setting, making money will usually involve something the mc is good at, perhaps have him meet some type of hard to persuade person whilst looking for a job, bet everything he has on his ability in your case learning ability, and use that to change that persons mind.... i.e, stubborn blacksmith thinking your a joke claiming that you can learn blacksmithing in only a few sessions etc...doesnt have to be a blacksmith can be anything like a librarian to a simple store clerk and such, just highlight his ability.... usually that is what authors do.

I just wanted to thank everyone for their suggestions
I think I've reached to a decision

Maili Well, it is kind of hard to justify how they get so powerful without a cheat >.<

Siterus make a guild, have him join, take quests. Done

Maili They're all cheats in disguse
Of course my character has an explanation about his cheat, but that doesn't change what it is, a cheat