Join a data center wide hunt Discord. Players also relay achievement FATEs there and you'll usually get a decent number of players showing up to help clear it.

For Crystal: Crystal's The Pursuit Hunts https://discord.gg/S8fKQvh
For all data centers: Centurio Hunts (FFXIV) https://discord.gg/dZTgnpv
There's also faloop.app that will relay the major FATEs. They have data center specific discords with links that can be found on their website.

If you're not a Discord user, try to find an active cross world hunt linkshell with room. They will sometimes spread relays there as well though most of the time it's limited to the major achievement FATEs that reward tokens and not the lesser achievement FATEs.

A lot of times I'll stumble across an achievement FATE when I'm leveling an alt or out doing hunt related stuff. I'll relay then stick around to help. It's very rare that not enough players show up unless the FATE has less than 10 minutes at the time I find it (and I don't bother to relay if it's less than 6 unless it's one that's quick and easy to clear). There are a lot of players looking to get their achievements and special items from those FATEs.