Is it wrong always and everywhere for anyone to believe anything on insufficient evidence? (W. K. Clifford) If so, the young would never be right to believe in the realization of their potentials. But they are right so to believe. If they didn't, none of them would ever have 'made it.' But many of us did. We made it, but only by believing in ourselves well beyond the evidence available. Give it your best shot, but don't piss and moan if it comes to nought. Take another shot, a different one.
For a development of this theme, see Is it Sometimes Rational to Believe on Insufficient Evidence?