I know it's possible to do things with users who have never interacted with your community, though I am not sure what they used to do it. No client I have used even has the basic moderation functions down very well, and through the website interface I have only seen mod actions appear within posts in communities I mod and nowhere else.
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It depends on the app or interface you are using. In Mlem there is an "Add Moderator" button in the moderation tab. I believe in the web interface it is easiest if someone posts, or comments, then in the three dot menu there is an option to make moderator.
Using Firefox point....well I don't know what they are up to now.
That would be the web interface, unless you are also using photon, Blorp, or one of the other front ends that are useable via the web.
But there is a high chance you are using the vanilla interface.

what does the strawberry and chocolate face look like?
Blorp dev here. Sounds like we have to rename the app to chocolate
I have no idea what you mean.