Wouldn't I be better off focusing on people I already know are awesome, and people I am introduced to?

This assumes you are good at detecting awesomeness, and are the sort of person that gets introduced to people.

I would hazard to guess that many 'unlucky' people have neither. (In fact, I would hazard to guess that many 'unlucky' people simply don't have a good social network or a good way to establish one, and lucky people are already following your protocol, leading to a strong Matthew effect).