Self-belief is something the Doctor knows quite a lot about, mostly because he has so much of it. He believes he has a purpose, and that he does what he does for a reason; perhaps the universe itself set him on his course and continues to guide him, sending him where he’s needed. After all, why else would he end up somewhere he didn’t intend to go, at exactly the right moment to save lives, defeat threats, solve crimes, prevent disasters, or free entire worlds from tyranny?
He’s fulfilling the role he was created for, and it’s so much fun!