Practice, practice, practice. Since you're willing to do the silly hat dance; some thoughts on the type of practice you could do: Program with your laptop hooked up to your TV to your empty living room, to get used to the feeling of being watched. Then have a close and trusted friend be in your living room and just sit quietly. Add a cafe background noise track playing[0]. After you're comfortable with that, stream yourself solving leetcode/whatever problems on Twitch. Doesn't actually matter if anyone comes in to watch you, but talk out loud and explain your thought processes as you work your way through each problem.
[0] eg https://youtu.be/gaGrHUekGrc