Yes, I know it’s Gene Roddenberry in our world, but in the TOS episode The Man Trap, Sulu says this to Yeoman Rand:
“May the great bird of the galaxy bless your planet!”
You can see it in this clip: https://www.youtube.com/watch?v=lk3tM4Ns3LY
There is also this Okudagram that appeared in two TNG episodes (The Naked Now and Conspiracy) and was clear enough on-screen to make it less than just a joke:
So it appears that there is something known as The Great Bird of the Galaxy, it has a human head, possibly a Starfleet delta, and it’s used in a saying that may or may not be an actual blessing.
So what was it? Was it an Academy joke? Was it a real religion? Obviously it was more than just something Sulu made up since there’s an entry for it on the Enterprise D’s computer (which seems like an odd thing to have if it’s an in-joke).
The Koala is apparently also canon since an omniscient being said it was there and Boimler saw it during a near-death experience.
Right. I think the real question is: How did Sulu know about it? I would love to believe that it was formless and Sulu just had a wacky belief, and upon hearing it said out loud it thought “LOL, OK then.”