The Young Avengers were the young successors to Earth's Mightiest Heroes after the events of Avengers Disassembled. The old guard had split apart, so it was time for a new generation of heroes to take over for them. Each of the team members initially took a name and costume that seemed to pay homage to an Avenger, though this later became less of the norm.
Many of the individuals who would become the Young Avengers have already been introduced in the Marvel Cinematic Universe. It seems almost inevitable that the Young Avengers will be introduced; it's only a question of how Marvel will do it.
7 The Old Guard Avengers Will Bring Them Together To Train Them
This approach seems the most likely, as it would allow for audiences to be introduced to these new characters accompanied by recognizable faces. Furthermore, the Young Avengers had their own version of the Vision called Jonas (who was the living armor of Iron Lad). The White Vision introduced in Wandavision could be the old guard Avenger needed to lead this team even if the White Vision isn't technically the Vision audiences already know.
Beyond that, Sam Wilson as Captain America, the Winter Soldier, Captain Marvel, War Machine, Doctor Strange, Scarlet Witch, Nick Fury, Hawkeye (though he's semi-retired) and Bruce Banner are all around and active, so they could also help train and guide a new team of heroes.
6 An Avengers Enemy Will Bring Them Together To Fight The Avengers
This eventuality also has a hint of plausibility thanks to the established lore of the Young Avengers. While the team never fought the Avengers in the comics, one of their founding members was Iron Lad. He turned out to be a young Nathaniel Richards, the true name of Kang the Conqueror.
Kang could potentially manipulate his younger self into making a Young Avengers team meant to take out the remaining active Avengers. Other than Kang, it's feasible that Baron Zemo, Valentina, Kingpin, or a new Norman Osborn (who was turning young superheroes into weapons during Dark Reign) would manipulate a crew of young heroes into fighting the Avengers.
5 They Will Unite To Take On The Dark Avengers Or Thunderbolts
It seems that Contessa Valentina Allegra de Fontaine (played by Julia Louis-Dreyfuss) is putting together some sort of Dark Avengers-like team with John Walker and Yelena Belova. It seems very possible, with the Sakovia Accords still seeming to be in effect, that the government will sanction its own superhero team that would be more brutal and morally flexible than the Avengers. On top of that, Baron Zemo is still alive and could potentially unite a Thunderbolts team to pose as heroes as he did in the comics.
In such a case, with the old guard heroes prevented from acting by law or force, the Young Avengers could easily rise to take on the Dark Avengers or Thunderbolts to remind everyone what heroes are supposed to be.
4 They're Already Here And United During The Five Years Between Infinity Wars And Endgame
This method seems less likely given that Young Avengers like Wiccan, Speed, and America Chavez were introduced after the events of Avengers: Endgame. However, it has been established that Cassie Lang and Kate Bishop survived the Snap, and it's possible that Eli Bradley and maybe even a young Kang could have already organized a team hiding in the shadows.
This would be a pretty big secret for Cassie to keep from Ant-Man and Kate to keep from Hawkeye, but retconning information in after the fact is kind of part and parcel with the superhero genre.
3 They Will Spiral Out Of An Adaptation Of Secret Wars
The original Secret Wars by Jim Shooter, Mike Zeck, and Bob Layton had several heroes taken off Earth for a period of time to fight on Battleworld for the amusement of the Beyonder. In Secret Wars (2015) by Jonathan Hickman and Esad Ribic, reality ended with the exception of a Battleworld made of Earths from different dimensions.
Either one of these premises would be fertile ground for the arrival of the Young Avengers. Either they unite to take on evil while the older heroes are fighting on the Beyonder's Battleword like in the original Secret Wars, or they cross over onto the MCU Earth through the interdimensional Battleworld of Secret Wars (2015).
2 They Will Be Found In The Multiverse Of Madness
America Chavez has already been shown in the trailers for Doctor Strange: Multiverse of Madness, and she was a Young Avenger during the team's second iteration. While many Young Avengers have already been introduced to exist on the MCU Earth, it's possible that other members will be found and join America in Multiverse of Madness.
Since much of the story seems to center around what Scarlet Witch did in Wandavision, it's feasible that Tommy and Billy Maximoff will return somehow by the end of this movie.
1 They Will Simply Assemble On Their Own To Replace The Avengers
Another likely possibility is a fairly simple and straightforward one: they will simply assemble to replace the Avengers. It seems likely that there will be another Avengers team, but that hasn't been confirmed yet. The New Avengers of the comics assembled shortly before the formation of the Young Avengers anyway.
Many of the pieces are already in place. America Chavez/Miss America is in Doctor Strange: Multiverse of Madness. An older Cassie Lang/Stature was shown in Avengers: Endgame. Eli Bradley/The Patriot made a brief appearance in Falcon and The Winter Soldier. Kate Bishop/Hawkeye made her debut with Hawkeye. Kid Loki showed up in Loki. Tommy Shepherd/Speed and Billy Kaplan/Wiccan were a central part of Wandavision. The new White Vision could be the Jonas Vision.
That only leaves out Hulkling, who could easily show up soon. Kang has already shown up, so Iron Lad would be easy to add. Though Ms. Marvel hasn't been a Young Avenger yet, she is joining the MCU soon. The Champions, of which Ms. Marvel is a member, have a lot of similarities with the Young Avengers, so it's not hard to imagine Kamala Khan being part of an MCU Young Avengers team.