Have you reached out to members of your Fleet Shard? It's not so much "by invitation only" (or at least, it shouldn't be), but by people who make an effort. I know for our Fleet Shard, we have an entire list of people's pay out times and we coordinate efforts so that someone who is in their "pay out hour" - that we don't attack them, so they can rise as far as they can to get the best pay out.
We can only do that if we know. You might have to make some effort to find out, though. You'll have to get the user's name and what guild they are in. Then go to SWGOH.GG and find that guild, and then find that user within that guild... so you can copy their ally code, so that you can then message that user in game and ask "Hey, can I join the Fleet shard chat?"
Yes, you will have to join discord - as we use this for communication. But in this game, guilds and shards are very active on discord. Again, it's about making an effort to be a part of a community.
My $.02 worth - take it for what's it worth.