Belief is a specific, visible bet you make on a person before the evidence fully supports it, not naive optimism.
When you hand someone a stretch task and say, out loud, "I think you can do this," you're giving them permission to try something they'd otherwise have talked themselves out of. Confidence you show in someone becomes confidence they borrow until they can carry it themselves.
The risk is believing loudly and then withdrawing support at the first stumble. Real belief survives the first failure, that's what separates it from empty cheerleading.
"I think you can do this, and here's specifically why: [the thing you've actually noticed]." The specific reason is what makes it land as belief instead of flattery.
Belief alone is not the whole job. Plenty of people are excellent individually and leave everyone around them exactly as they found them. A smaller number consistently make the people they work with sharper, and it rarely takes a formal mentorship program. It shows up in small, repeatable moments: explaining the reasoning behind a decision instead of just handing over the decision, so the lesson transfers. Teach the why, not just the fix, and the next time it comes up, they don't need you.
Pick one person on your team who's playing it safe. Give them a task slightly above their comfort level, and tell them directly why you think they're ready for it. Then watch for the first stumble, and don't pull the task back when it comes.