Proving the doubters wrong is overrated. Most of them already moved on. Prove yourself right instead.

The audience you are arguing with in your head is mostly not watching. People who doubted you did it in passing and went back to their own worries, so the scene you are picturing has nobody in the seats. Working to be right about yourself is different, because that audience never leaves.

Name the thing you privately suspect you could do. Do a small version of it this month without telling the people you wanted to impress. Notice how the proof feels when it is only for you, and whether you still need them to see it.