I think it would be Spider - Man. He's closer to her age in a way compared to the other Avengers. He can understand her more easily, like the things she likes, the new trends, etc. And he has that friendly neighborhood hero vibe that would make the girl feel comfortable around him quickly.
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.
Thor would be the most likely. Since Thor has a connection to Norse mythology already, he would be familiar with Sleipnir. He might see Sleipnir as a symbol of his home realm and would quickly bond with it. They could communicate in a way that the other Avengers can't, sharing stories of Asgard and the great battles there.
There could be a human character, perhaps a teacher or a neighbor who notices the strange situation with the Cullens and the little girl. This character could add some extra drama as they try to figure out what's really going on with this family that seems a bit different. They might suspect the Cullens are up to something not quite normal and start to investigate, creating more storylines.
Well, perhaps the little girl has some special power that the Cullens notice. So they decide to take her in to protect her from those who might misuse her power. For example, she could have the power to predict the future in a very unique way that even the Cullens find fascinating.
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.
I think Thor would have a strong bond with Fem Harry. He comes from a world of magic himself, so he would understand her magical abilities better than some of the others. Also, his big - hearted nature would make him very protective of her.
One idea could be that the two broke girls, Max and Caroline, struggle at first to adjust to having a little girl in their lives. They might face financial difficulties in providing for her but find creative ways to make it work, like using their cupcake business to earn extra money for her school supplies.
Thor would be a likely candidate. Since he is Loki's brother, he already has a connection with him. Thor might be the one to convince the other Avengers to give Loki a chance and be the first to reach out and try to befriend him in this new situation.
In Batman fanfiction involving a little girl, it could be about various scenarios. Maybe she is a young protege that Batman takes under his wing to train in the ways of justice. For example, he might teach her self - defense and detective skills, just like he did with Robin.
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.