It turns out that Captain America actually formed the New Avengers a decade before fans think he did. This all took place in a timeline depicted in 1995’s The Last Avengers Story. It’s a two-issue prestige-sized series written by Peter David and illustrated by Ariel Olivetti.
The Last Avengers is a The End type story that came out years before The End was even a thing. The dystopian timeline takes a turn for the worst when the government finally decides to take care of the super-villains by enlisting the heroes to do a massive villain round-up. Once they were all in custody, the government executed all the villains, unbeknownst to the heroes who captured them. When they learned about this horrific use of their heroism, the distraught Avengers disbanded and went their separate ways. Hank Pym considered quitting being a hero. When he asks Captain America what it would take to make him quit, Cap responds, “Death. Maybe.”
He goes on to run for president and wins. One thing Cap does as president is form a team of New Avengers, which is largely made up of original characters made for the story. Many believe this team is largely symbolic, as the vast majority of villains have already been eliminated. There is nothing for the team to do but hang around the base, an inoperative nuclear power plant, and play cards. In fact, the team is only in one scene before the book’s main foe, Ultron 58, drops a bomb on the building, wiping them all out.
This is a very different situation from the more-well known (and successful) New Avengers team Cap forms in 2005’s New Avenger’s #3. The brainchild of Brian Michael Bendis, this team is more closely aligned with the formation of the original Avengers. After the Avengers were disassembled following Scarlet Witch’s mental breakdown, a group of heroes came together at the super-villain prison The Raft to stop a breakout. This natural “coming together” reminded Cap of how the original Avengers came together to fight Loki, and he used the moment to implore Iron Man to form a new team.
The contrast between these two situations is telling and very reflective of the stories in which they are told. In The Last Avengers Story, Cap orders a team to be formed as president, a team he isn’t even involved in. It’s forced and a largely unnecessary decision compared to the main 616 timeline, where Cap’s inspired to create a team from an organic need to stop a threat. This is probably why Captain America's story in The Last Avengers is a tragedy and his New Avengers one is largely fueled by hope.