The Super-Key To Fort Superman
This is a well protected place, but, Superman's friend, Batman, found a way to sneak in, to play a prank on Superman, and remind him of the anniversary of the day Superman first arrived on Earth from Krypton.
But, this story focuses on Superman having a rich past, so, it obviously isn't the start of the Silver Age Superman, so, let's continue the look back to find a few more distinguishing characteristics....and the true first appearance.
Superman's Pal Jimmy Olsen
Jimmy got first used his signal watch, which he could use to call Superman in this issue, as well as the introduction of the Flying Newsroom, which allowed Jimmy to quickly get into the action (or trouble), so he could capture photos of breaking news...and later issues introduced things like Jimmy's own super-hero identity of Elastic Lad, as well as Morgan Edge and the beginnings of the battle for control of the Fourth World with Orion and Darkseid.
the concept of Earth-1 and Earth-2 was introduced in Flash #123 (September, 1961) with the return of the Golden Age Flash Jay Garrick (and, soon after that, the return of the Golden Age Justice Society, the counterparts of the Silver Age Justice League of America).
World's Finest Comics
These team-ups predated their founding of the Justice League of America (along with Flash Barry Allen and four others: Wonder Woman, Aquaman, Martian Manhunter and Green Lantern, and their first published battle against Starro the Conqueror), but their friendship had begun even before that.
first meeting of the Silver Age Superman and Batman....that happened in a flashback tale told in World's Finest Comics #94 (May-June, 1958)
Superboy was another unique factor in the life of the Silver Age Superman; the Golden Age Superman did not have adventures in costume as a boy, only slowly learning of his powers over time (including an adventure where Superboy crossed over from Earth-1 to Earth-2, to help teach a confused young Clark Kent on that world a little bit about dealing with his Kryptonian powers).
Justice Society of America and Seven Soldiers of Victory, as well as many unaffiliated heroes....which were retroactively put into the All-Star Squadron). Superboy's adventures continued from More Fun Comics to Adventure Comics, where he met a literal Legion of Super-Heroes in Adventure Comics #247 (April, 1958), a team of heroes from the future who recruited the lad to join him (and a team which, in the real world, predated the Justice League of America).