The "admin" user joined on the 8th of June last year and I'm guessing that was the initial account used for setup, so probably that date the instance started
ICANN lookup is another source. According to them, aussie.zone was registered on 2023-06-08 05:26:09 UTC.
So, yes. 8th of June would be a date I'd endorse. It's also @lodion's signup date. The oldest "regular" user is @BadlyDrawnRhino, who signed up on June 16th. You could argue that was the day we opened to the public and is more appropriate.