Belief does not win arguments with doubt. It moves first, and the doubt follows it around complaining, and gradually has less to say.
Anyone stepping onto a frozen lake knows the feeling. You test the edge, you shift your weight, and then you go. Not because the fear has gone but because the fear has been given a smaller job.
Acting on your own behalf while unconvinced is the ordinary form of this. It is what most people mean when they say they believe in themselves.