I just finished setting up the hardware infrastructure to start hosting but I cannot find any specific information in the official documentation on how to set up a public Invidious instance. I understand the guide as far as just hosting an instance and watching YouTube through that goes, but how do I, for instance, give it a publicly searchable domain name that - in the best of worlds - is listed on Invidious’ website?
I assume there is a better way than to start posting my instance’s IP address throughout any forums that I might be active on?


As diminou mentioned, do your research before you go down this road. You can also open yourself to DMCA takedowns if you aren’t careful.
See: https://docs.invidious.io/hide-instance-behind-proxy-server/
It would be better for you to just run a private instance initially. You can use tailscale if you want to be able to access it remotely. That’s the safest way to start out.
Edit: There’s a tutorial here if you are intent on doing it: https://fedfree.org/docs/http/arch-invidious.html