Btukfyl

Is there a word or phrase to describe someone who is NOT formally trained at something — yet he/she IS GOOD AT IT?

The person could be good at drawing/art, or mathematics, or carpentry, or boxing, or a musical instrument, etc.

I thought the word for what I described is "UNTUTORED" because according to Collins Dictionary:

👉 UNTUTORED = adjective ▸ "If someone is untutored, they have not been formally trained to do something, although they may be quite skilled at it." 👈

One of the two example sentences Collins offered was:

➔ 'This untutored mathematician had an obsession with numbers.'

So because of Collins's definition, I took "untutored" as having to do with innate abilities, like a kid who happens to draw so great, or have a knack for a musical instrument — BEFORE any formal training.

But the problem is NO other dictionary defines "untutored" this way. ALL the others define it along the lines of "lacking in schooling".

So any help in describing «being good at something without being trained in it» would be appreciated.

a natural-born X TFD idiom

Possessing an ability innately. The term is always used as a modifier
before a noun.

As in:

My daughter is a natural-born chef.

Often these sorts of people are called "naturals" -- "Wow, your kid is a real natural at basketball! I can't believe he's never had a coach!"

Such people, especially children, may also be called "prodigies", which mildly-suggests that they were pretty good before training, but doesn't rule out training per se. Some English speakers have adopted the German term, wunderkind.

I think you're correct in shunning 'untutored' for this application.

In some contexts "self-taught" might be appropriate.

Well! It's taken me a little while combing through some dictionaries and thesauruses, I believe "Innate" is the word you are looking for.
Innate: adjective:
1.) Existing in an animal or a person from birth; congenital; inborn
2.) Instinctive; Not Learned
3.) (In rationalist Philosophy)(of Ideas) present in the mind before any experience and knowable by pure reason
Instinctive; Intuitive; Natural; Prodigy; Constitutional

There is this interesting concept called autodidacticism (in plain English, it simply means self-education or self-teaching) that means you have received no formal education at all, but because of your great yearning for education and your natural talent, you were able to acquire the necessary skill and knowledge to become exceptionally good at whatever it is that you're doing. Probably, one of the best examples of autodidacts (a person who practices autodidacticism) was the brilliant Indian mathematician Srinivasa Ramanujan who, although had no formal education in mathematics, managed to become one of the great mathematicians of the early 20th century. Here's what Wikipedia says about this incredible individual:

Though he had almost no formal training in pure mathematics, he made substantial contributions to mathematical analysis, number theory, infinite series, and continued fractions, including solutions to mathematical problems considered to be unsolvable.

I like the natural and natural-born answers for if the person has had no training at all, but I would also suggest autodidact for someone who has trained themselves to a level of great skill without the benefit of formal training by others.