I am looking for a word or group of words to describe someone who just started doing something, but is already very good at it, or a beginner without faults. For example, it could be used in this sentence: "Although Mary had just started playing Tennis, she had already won 3 tournaments; Some could say she was a ______".
You can use the word "natural" either as an adjective or as a noun, to describe the person and their skill or the person themself.
attributive (of a person) having an innate skill or quality.
‘he was a natural entertainer’
natural (noun) A person having an innate talent for a particular task or activity.
‘she was a natural for television work’
Oxford Living Dictionaries
Another is the word "gifted".
Having exceptional talent or natural ability.
‘a gifted amateur musician’
Oxford Living Dictionaries
If you want another noun describing the person, then "prodigy"
often with modifier A young person with exceptional qualities or abilities.
‘a Russian pianist who was a child prodigy in his day’
Oxford Living Dictionary
More often than not prodigy is used with minors or children.
"He was a pragmatist and quick learner. He was skilled at picking up ideas from others and making them his own." (Lawrence M. O’Rourke, Row House to White House, 2012, p.3319)
"The quick learner has what is called in ordinary terminology, the power of concentration. All the available cerebral energy seems to participate in ..." (William Henry Pyle - 1921)
"You had no experience as a woman, but you were full of spirit and a quick learner." (Gary Jonas - 2011)
Also, fast learner
Although Mary had just started playing Tennis, she had already won 3 tournaments; she was a real talent.
(someone who has) a natural ability to be good at something, especially without being taught
Source: Cambridge Online
[: phenomenon; especially : a person of phenomenal ability or promise]
If an adjective would suffice, I would say that she has a knack for tennis:
1 An acquired or natural skill at doing something.
‘he had a knack for communicating’
Depending on your context, you might call this person a whiz kid:
a young person who is outstandingly skillful or successful at something.
"a computer whiz kid"
In some contexts, the term rising star might be appropriate.
If Mary was dedicated to her tennis career, and it was understood that she was already gifted for a beginner and on the way to success, it could be used here.
rising star: a person or thing that is growing quickly in popularity or importance in a particular field
rising star: a person who is likely to be successful
However, it wouldn't be an appropriate term for something less important than a career or primary hobby - for example, if someone succeeded in their first cookery class, but wasn't particularly dedicated to cookery, the term wouldn't be appropriate.
Yet another option: wunderkind
Prodigy works. The comments about prodigy only applies to children are not entirely true. BJ Penn was widely referred to as 'the prodigy' and he learned his craft after highschool.
Precocious is another possibility
In dancing we use "advanced Beginner"