I noticed that the Orville does not seem to use any dating system in the show. I'm sure because they want to keep the episodes more episodic , so they gloss over that stuff.
Well, they don't do those kinds of expository voice-overs very often on the show - few or no logs, journals etc. The stardate was only invented to give an illusion of verisimilitude to that kind of thing, not because it serves any necessary "in-universe" function.