built-in output doesn't show up

Sometimes if one restarts in Safe mode, those kinds of things seem

to fix themselves on the next 'normal' startup.

Or you could try reset NVRAM using exact instructions in article.

Good luck!🌻🐝

Have you recently had an external output like headphones or speakers attached? Some aftermarket devices have out-of-spec plugs and can jam the audio port in the muted position. It is not a matter of brand quality. I've had quality headphones jam the plug and cheap "no-name" devices work perfectly.

Not sure which MBP you have. On older ones, a red light would glow in the port if the mute switch became jammed.

If you see a light insert the jack about 90% of the way and GENTLY wiggle it up, down, right, and left. Remove and see if the light goes out. This may need repeating to achieve success, but it behooves you to keep trying because, on some older models, Apple's fix for this was a new logic board!