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.
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.
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.
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.
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.
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.
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.
A really interesting one is 'Avengers vs Hydra: A New Perspective'. It presents a different view of the age - old conflict. Instead of the usual fight, it explores the idea of some Avengers having a more nuanced view of Hydra and how that affects their actions and the overall dynamic within the team.
Fanfiction explores it in many ways. For example, some might show a reluctant alliance between an Avenger and a Hydra operative for a common goal. This shows that the relationship is not always black and white.
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.