When last we left off, superhero comics had waned and been replaced by horror comics. In the Golden Age of Marvel, most heroes inhabited separate worlds, rarely crossing over, with two exceptions: the Human Torch/Sub-Mariner fight and the short-lived All-Winners Squad. When Timely Comics became Atlas, they tried to revive Captain America, the Human Torch, and the Sub-Mariner, but it was short-lived. It wouldn't be until 1961 that Marvel was able to put out superheroes again.
The Silver Age of Marvel is generally accepted to have begun with Fantastic Four #1 (November 1961) and ended with The Amazing Spider-Man #122 (July 1973), also known as "The Night Gwen Stacy Died." In between, it was filled with numerous superheroes and numerous crossovers.
In fact, while the Golden Age maintained separate worlds for their heroes, the Silver Age was practically built on having a shared universe. In only the fourth issue of their series, the Fantastic Four encounter an amnesiac Namor and once he regains his memories, they scramble to stop him from unleashing the monstrous Giganto upon New York.
In fact, it became something of a trope to include cameos of other heroes in different books. In the very first issue of The Amazing Spider-Man (March 1963), Spider-Man auditions for the Fantastic Four by trying to break into the Baxter Building. The heroes all inhabited the same world and they showed this to the readers constantly.
As shown previously, The Avengers #1 (September 1963) wasn't the first comic to have previous heroes team up, but it did provide an opportunity to use characters that didn't have their own books: Ant-Man, for example, was first seen in Tales to Astonish #27 (January 1962), "The Man in the Ant Hill." It was primarily a weird science fiction tale, but they brought back Hank Pym eight issues later as the superhero Ant-Man (and, later, his girlfriend, the Wasp). The Ant-Man/Wasp stories, though a regular feature, never really sold well, so Lee and Kirby decided to team them up with other heroes. Thor was in Journey Into Mystery and Iron Man was in Tales of Suspense, but The Incredible Hulk had been cancelled after six issues. Bringing together these heroes provided each of them with a spotlight.
The Fantastic Four Annual #3 (1965) provided a treasure trove of cameos from various superheroes and supervillains. Just take a look at the character list:
Fantastic Four [Mr. Fantastic [Reed Richards]; Invisible Girl [Susan Storm]; Human Torch [Johnny Storm]; Thing [Ben Grimm]]; Avengers [Thor; Captain America [Steve Rogers]; Iron Man [Tony Stark]; Hawkeye [Clint Barton]; Quicksilver [Pietro Maximoff]; Scarlet Witch [Wanda Maximoff]; Wasp [Janet Van Dyne]]; X-Men [Cyclops [Scott Summers]; Marvel Girl [Jean Grey]; Angel [Warren Worthington III]; Beast [Hank McCoy]; Iceman [Bobby Drake]]; Daredevil [Matt Murdock]; Hulk [Bruce Banner]; Sgt. Fury [Nick Fury]; Spider-Man [Peter Parker]; Two-Gun Kid; Android; Attuma; Black Knight [Nathan Garrett]; Cobra [Klaus Voorhees]; Crimson Dynamo; Doctor Doom [Victor Von Doom]; Dragon Man; Executioner [Skurge]; Enchantress; Grey Gargoyle [Paul Duval]; Kang; Leader; Loki; Mandarin; Medusa; Mister Hyde [Calvin Zabo]; Mole Man [Harvey Elder]; Red Ghost [Ivan Kragoff]; Red Skull; Sub-Mariner [Namor]; Super-Skrull; Thinker; Unicorn [Milos Masaryk]; Wizard [Bentley Wittman]
These were just cameos though. The first true crossover — where a story starts in one book and ends in another — began with Tales of Suspense #80 (August 1966), with a story starring Iron Man and Namor (somehow, Namor always seems involved with these crossovers). The story concluded in Tales to Astonish #82.
Other crossovers included the "Daredevil-Dr Doom swap" (Daredevil #37-38, Fantastic Four #73), the "Terrible Trio" (Sub-Mariner #14, Captain Marvel #14, Avengers #63), and, finally, the "Formation of the Defenders" (Doctor Strange #183, Sub-Mariner #22, Incredible Hulk #126), where the Defenders (minus the Silver Surfer) end up fighting the Undying Ones. This crossover led to them having their own adventures in Marvel Feature and then their own book.
Bigger crossovers started happening in the '70s with the epic "Kree-Skrull War" (Avengers #89-97, Amazing Adventures #5-8), the "Avengers-Defenders War" (Defenders #8-11, Avengers #115-118), and the "Thanos War" (Iron Man #55, Captain Marvel #25-33, Avengers #125, Marvel Feature #12, Daredevil #97-105 — Jim Starlin was able to really sneak this one into all the books he was writing). But it would be until after Gwen Stacy died, when the Bronze Age started, that the crossovers really started happening.
That's when it was time for the Contest of Champions...