Yours truly has won 218 of his last 219 games, and has never had an official rating.
Great Players Without Official Ratings

He got that rating for his first ever FIDE tournament in Banja Luka 1979.
However, he had been playing tournaments in the USSR for half five years or so.

But can't edit on my phone.
Blarg!!!

Does Jeff Sarwer have an official rating?
As of now - 5 years later - Sarwer has a FIDE rating 2246 and a finnish rating 2259. He is an FM. He occasionally plays in finnish tournaments. His best result from recent years is probably 5/9 in the GM-group of VI ShakkiNet international in 2015 which earned him an IM-norm. He has also had some bad results, perhaps most notably scoring a terrible 0/9 in finnish team ch. 2015-2016.
Much more common is someone that's never been rated who THINKS they are some sort of super strong player.

Savon was only an IM when he won the USSR Championship in 1971. He was chosen the next year to represent the USSR in the Skopje Olympiad. In case you're in any doubt about the magnitude of this achievement look at this thread and the 1971 Championship final results table with the names of participating players in it (supplied by batgirl), as well as a list of his team mates at the Olympiad (supplied by me).

I know a lot of people in India who play great chess but don't participate in tournaments due to various reasons

I know a lot of people in India who play great chess but don't participate in tournaments due to various reasons

I know a lot of people in India who play great chess but don't participate in tournaments due to various reasons

they quit chess because they finally realized there is no money in it
Top 10 players are millionaires. but they probably got good really young and had financial support.
they say people ranked top 100 to 11th can make 100,000 a year. but it is really tough. they have to get a sponsor or they make a lot of lessons.
but even being a successful coach is tough too. GMs charge $80 an hour for lessons. who has that kind of money? so it is not like they are making it.
everyone else is trying to scrape by with a liviing which i think is probably 20,000 dollars per year. you can make more money with another profession.
During my college club days these guys from the ghetto used to walk several miles to show up, and some of them were definately in the 1800-2000 range. That being said, they played OTB chess all the time, either with each other or with the college club (which boasted a few masters). Its not inconceivable that every major city has a few unrated expert or master-level strength players. GM is another story - It takes serious dedication and training to get there.
Kind of like how being a great athlete and street basketball player won't prepare you at all for the NBA regardless of your talent - you need coaching to get yourself at that level.

Unrated genuine expert-level (FIDE 2000 and up) players - yes, you do see them in major cities. Not too many of them, to be sure - but here and there yes.
Unrated master-level players, as in FIDE 2200 and up (the lowest master category) - this must be very very rare. I never met one, and I've been places.

Just to complete my above post - those - "natural" players who are expert-level without playing tournament games, have all read books, analyzed games, worked together with other players - they are part of a chess context, not some kind of "noble savages". One also can't be absolutely sure that indeed, they never played slow time-control games, officially or otherwise. They have certainly been part of a certain chess community for years in order to become that strong, tournaments or not.
This myth of the "great natural talent who never played competitively" implies a genius who grows up in isolation, without access to any chess materials or culture, except for his bright mind.
I never met anybody like that who was stronger than 1200. I also don't expect to meet such people.
There used to be an old man, who was teaching me chess, or mostly how to lose against him. Playing chess in the park most of the times. Well long story short one day few guys from chess club say Tom why not come and join this competition we have organized the next few days. He shows up and beats everyone and draws against and IM he went on to win first place. In the open where he competed top players ranged from 2100 to IM strenght. He was a great chess player. attacking and loved kings gambit. RIP Tom
I have never played a single tournament otb-game nor attended to a chess club. But for 20 years ( started playing in chess.net when I i went to university back then, other than that I haf been playing just at home with my siblings) I have been playing quite regularly a few blitz games a day. I have a couple of chess books and do occasionally watch youtube chess videos. I'm not that strong, but do now and then beat titled players in 5 min Blitz. Of course it's a very different world to OTB-games, for sure, but I dream of taking part in club chess as well as tournaments when i do reach retirement after 25+ years. It would be exciting to find out my actual OTB strenght. Due to my duties I don't have such luxurious opportunity for a while.
+1 Lasker 1900