Why is Ann Sheridan . . . .
. . . . billed so near the top when she's only in the first 10 minutes of the picture?
Gloria Dickson had 5x the screen time.
What gives?
It was the studio system. It is not about screen time as much as star treatment.
Sheridan signed with Warner Brothers in 1936. They gave her a nickname, which was one of the first steps in the star making process. Just the year before this picture, she had her first substantial role in Angels With Dirty Faces. Once designated as a star, the studio would always treat her that way. And that meant star billing, regardless of the size of the part.
For a later example from a different studio, watch the opening credits of Singing in the Rain. Rita Moreno gets a full screen, stand alone credit, although she has a very small part. Most people don't even remember that she is in that film. But MGM had her under contract and this was a way to build her up.