Mozart composed from the age of five and performed before European royalty.
Not many grownups can do that.
What is a noun expressing a very young person who has advanced skills even higher than adults?
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Someone with a very great ability that usually shows itself when that person is a young child
It should be mentioned that 'child prodigy' is also a noun, but applicable to a young person who is a child (Magnus Carlsen became a Grandmaster, the highest norm of Chess when he was 13 years old and thus was labelled a child prodigy).
one who succeeds in a competitive or highly difficult field or profession at an early age
This is a German loanword, with the original pronunciation, and the classic example is Mozart.
The calque wonderkid also exists, but is a primarily-British word for an excellent young athlete. The Collins dictionary gives a broader definition, but when you look at the list of examples, they’re all about athletes.
(especially of children) showing mental development or achievement much earlier than usual
Other answers provide nouns for that young person. If you need an adjective, this would be your best choice. "Prodigy" as a noun describes the young person, but the adjective "prodigious" merely describes something which is exceptionally large or well-developed and does not reflect the OP's requirement that the development is exceptional for their age.
A more specific version is "enfant terrible" (French, lit. "terrible child").
While originally having the meaning of a child who embarrasses their parents by being very blunt and straightforward, now
it implies a successful, and often young, "genius" who is very unorthodox, striking, and in some cases, offensive, or rebellious
While this might not work very well in your specific example, it can be useful for others, and I think makes a good addition to the existing answers.