Supergirl's first appearance, depending on which Kara Zor-El you're talking about, is Action Comics #252 (1959) for the original, Superman/Batman #8 (2004) for the one actually pictured here, or Supergirl #1 (2012) for the most recent revision.
Crisis on Infinite Earths #7 features the original 1959 debuting Supergirl on the cover... dead, in Superman's arms.
If you're going to do geek porn, get the details right.
Supergirl's first appearance, depending on which Kara Zor-El you're talking about, is Action Comics #252 (1959) for the original, Superman/Batman #8 (2004) for the one actually pictured here, or Supergirl #1 (2012) for the most recent revision.
Crisis on Infinite Earths #7 features the original 1959 debuting Supergirl on the cover... dead, in Superman's arms.
If you're going to do geek porn, get the details right.