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.