That is extremely difficult to answer, because no one has ever made it clear just how the stardate system actually works. However, we do have some speculation. Based on the twenty-fourth century system from The Next Generation, Deep Space Nine, and Voyager, (plus some fuzzy math) we can get Stardate -374431.5. Yes, that's a negative number. Using the stardate system from the new movie that came out this month, the answer would be a simple Stardate 1949.158 (June 7th is the 158th day of the year). If you're using the five-digit system from the Original Series, you can just make up any number you want--there was no rhyme or reason to that old system.