Let’s start with the premise that self-confidence leads to greater success.  (Now, you may object because most of the highly self-confident people you know are not as good as they think they are.  But the premise is simply that they are more successful than they would otherwise be, not that their self-confidence is fully validated.)

Is it because confidence by itself makes you more successful?  You can do some interesting behavioral economics with that assumption but here’s another channel that requires less of a leap.  When you are confident in yourself you try harder, you take more chances, you let your intuitions run.  But that by itself doesn’t make you any more successful than the next guy.  Indeed it probably will make you less successful because your intuitions are probably wrong.

But it means that you will find that out sooner.  And if you are confident enough, when your first foray fails you will believe in yourself enough to regroup and try again. Even if your confidence doesn’t make it any more likely that these successive attempts pay off, you will still be more successful in the long run because you will learn faster what doesn’t work, and those lessons won’t demoralize you.

And once we have this, then it follows that confidence per se can make you more successful.  Because confidence signals this ability to roll with the punches and that will be rewarded by others.