So, in Rebirth (And New 52) how did she get the staff? Jack was born pretty late for a WW2 era Hero's kid already, so you cant really push it any further. And retiring to raise his kid puts a solid timecap on his adventures. So in universe he'd be passing the staff on the same time it happened IRL. But Courtney is still a teen in 2017. Was there a whole other Starman/girl having adventures in the 2000's or did Jack just wait a long ass time?
And this isnt even getting into how confusing her presence gets with the JSA being forgotten/never existing when her origin is so strongly linked to it.