I think global is a given. There’s no avoiding that; and what kind of community would we be if we said ‘no, sorry, you can’t join because you’re not from around here’.
An online community can be both big and small. If it’s conducted in the public sphere, like here, you can have a small group of dedicated users who stick around, and a large number of lurkers and people who pass by.
But in the end, what we want is people to talk to and getting to know people beyond just face facts. You don’t need much to do that other than perseverance.