A Super-Girl is introduced in Superman 123 (Aug. 58) by Binder, Sprang and Kaye, but she is not the one who would shortly gain her own series in Action Comics.
Jimmy Olsen is given a magic wishing stick, and the stories three chapters each detail one of the three wishes the stick gives him. The first chapter sees Jimmy bring to life a Super-Girl, to be a companion to Superman.
Aside from the red skirt, this Super-Girl is identical to the one that would be formally introduced the following year. But in this story she and Superman are romantically involved, to the dismay of Lois Lane.
But the two find it difficult to work together, and Super-Girl almost winds up exposing Clark’s identity.
In the end, she sacrifices herself to save Superman from kryptonite. And this was only the first chapter!
The second chapter is a bit of a let down. The wishing stick gets stolen, and the bad guys wish for Superman to lose his powers. Superman has to survive until Jimmy gets the stick back, and cancels the wish.
The third chapter sees Jimmy write down his wish, only to screw up a word, and instead of wanting Superman to meet his parents, he instead wishes for Superman to mate his parents.
The story does not explore that concept nearly as fully as it might. There are no forced breeding chambers, for example. But it does have some similarities to Back to the Future, as Superman has to bring together Jor-El and Lara.
The two are working undercover for the Kryptonian version of the F.B.I., but get rounded up and sentenced as criminals. They are shot out into space to be reformed by crystals over hundreds of years – an improvement over the method used on Mala and his brothers, of simply being shot into space permanently. Obviously, this story pre-dates the Phantom Zone.
In this story, there is mention of an identity brand that all Kryptonians have, but this terrifyingly authoritarian notion does not get carried forward.