You need to work hard first. Whether that is through full time employment or your own business, doesn't matter. Forget investors. No one will give you money. You are nobody right now.
Full time job for even 2-3 years is not a bad thing. I run my own business and wouldn't trade it for anything but I worked in the corporate world for 10 years and gained a lot of valuable experience. Not saying you should do the same path but you need to start somewhere.
"My biggest fear is mediocracy"
Working at a full time job doesn't make you mediocre. Not everyone is a Zuckerberg. In fact, it will teach you real world skills, you will meet smarter co-workers and people in the real world, learn lot of skills like conflict resolution, negotiating etc.
"biggest wish is to contribute to something meaningful and useful to others"
Yea, the problem is that you have no experience in anything so you wouldn't know what is meaningful and useful to others. Get a job. Get some experience. Work with a few people for at least 2-3 years and then figure out a path for yourself.
"Otherwise my existence makes no sense"
Lol at this but I understand that at 21, this seems normal. Your existence makes plenty of sense. But go grind first. Get a job. Learn a trade. Whatever. These thoughts will be meaningless once you have more maturity.