Perhaps the girl was kidnapped by Hydra to use as bait for the Avengers. But when the Avengers find her, they see through Hydra's plan. Instead of leaving her, they rescue her. This could lead to the girl having a strong bond with the Avengers, especially those like Captain America who have a soft spot for the underdog. She could then grow up to be an important part of their team or at least an ally in the fight against evil.
In the fanfiction, it might be that the little girl is a key to unlocking some secrets of Hydra. The Avengers, in their quest to dismantle Hydra completely, stumble upon her. She could hold the knowledge of hidden Hydra bases or their future plans. So they take her in to figure out how to use this information against Hydra.
The Avengers would likely be very protective of her at first. For example, Thor might use his strength to keep her safe from any immediate threats. Iron Man could use his technology to check if she has any tracking devices on her or if she's been poisoned by Hydra.
Captain America could be the main character. Since he has a long - standing history with Hydra (in the sense of fighting against their evil), he could be the one leading the charge to uncover and stop the Hydra experiment. His strong moral compass would make for an interesting dynamic as he tries to save those affected by the experiment.
Well, it could be about the Avengers recruiting the girl. They might see her powers as a great asset in their fight against evil. Maybe she has some sort of unique power like telekinesis or the ability to control nature. The story could focus on how she adjusts to being around the Avengers, learning from them and them learning from her too.
Well, maybe the little girl is a huge Avengers fan. One day, she gets into some sort of trouble, like being chased by bad guys who are after her unique abilities that she doesn't even fully understand yet. The Avengers find her and see her potential. Tony Stark might be the first to be charmed by her spunk and intelligence. So, they decide to take her in, protect her, and train her to be a part of their team in the future.
Betrayal is a common theme. For example, an Avenger might be secretly a Hydra agent, leading to a sense of betrayal among the team members.
In such a fanfiction, it could lead to some major plot twists and character developments. The Avengers' loyalties and actions would likely be completely different.
Perhaps there is a magical artifact in the Harry Potter universe that Hydra believes can give them ultimate power. They send agents to steal it, but the Avengers also learn about it. The two groups end up in a race to get the artifact, and along the way, they both have to deal with the magical defenses and creatures in the wizarding world. Harry Potter and his allies then have to decide who to trust - the Avengers who seem to have good intentions but are from a different world, or Hydra which is clearly evil.
Perhaps in the 'avengers of hydra fanfiction', Hydra has developed a new super - weapon that can neutralize the Avengers' powers one by one. The story could follow the Avengers as they scramble to find a way to counter this weapon while also dealing with Hydra's attacks on various cities. Or, there could be a plot where a powerful Hydra agent uses magic to possess some of the Avengers and make them do Hydra's bidding, and the remaining Avengers have to find a way to break the spell.
Definitely the Avengers members like Captain America, Iron Man, Thor, Hulk etc. would be main characters as they are the core of the Avengers. On the Hydra side, characters like Baron Wolfgang von Strucker could be prominent. Also, there might be some original characters created specifically for the fanfiction, perhaps a Hydra scientist who is behind a new and dangerous experiment targeting the Avengers.
One idea could be a crossover where Hydra discovers the wizarding world in the Harry Potter universe and tries to use magic for their evil purposes. The Avengers somehow get wind of this and team up with Harry Potter and his friends to stop Hydra. Maybe they have to battle magical creatures that Hydra has corrupted with dark magic.