Originally Posted by
Bat-Meal
Since Oracle has already been mentioned in the Arrowverse, but there's been no mention of a past Batgirl, and in an interview the lead writer mentioned that Babs and Gordon exist - it looks like Babs went straight to Oracle and was never Batgirl in this universe.
Nightwing was mentioned somewhere too, I heard, though from some book or something, so might not be cannon.
But if Kate was a child when Batman was established and known, Oracle was mentioned long before Batwoman debuts (whichever season of Arrow Felicity becomes Overwatch), and the radio announcer joke-speculates that Batman (when Batwoman is starting-out) missed catching a criminal to attend Robin's highschool graduation - makes you wonder which Robin the Arrowverse was up to (2nd or 3rd?).