After a few years in which the Legion of Super-Heroes appeared with increasing frequency as guest stars in various Superman books, they finally got their own series, beginning with Adventure 300 (Sept 62), with a classic cover by Curt Swan
The story pits them against a robot built centuries earlier by Lex Luthor, which has the ability to activate the powers of the various Legionnaires and use them against each other. Although nine Legionnaries are shown on the first page, only Cosmic Boy, Lightning Lad, Saturn Girl and Sun Boy have roles in the tale.
Superboy is very much the star of the story, though it’s Mon-El who saves the day, temporarily released from the Phantom Zone. He joins the Legion in this tale, but still much return to the Zone at the end, until a permanent cure is found for his lead poisoning.
The World Wide Police appear in this story. They are usually considered a forerunner of the Science Police, although looking at the dangerous craft they fly I think it just as likely that they died in those machines and were replaced by Science Police who were smart enough to build safer airships.