In many fanfictions, Snape meeting Hermione as a baby is a rare occurrence. Usually, the focus is on their interactions during her school years. However, there are always unique takes in the world of fanfiction.
In some fanfictions, such a plot twist might exist, but it's not a common or canonical occurrence.
There might be. Fanfiction is a vast world where all kinds of strange and interesting ideas are explored. But it goes against the general tone and relationships established in the 'Harry Potter' books. Hermione is more closely associated with Ron, and Snape has his own complex story that doesn't involve this kind of relationship with Hermione in the original work.
Perhaps the author of the fanfiction wanted to create drama and tension by having Hermione's mind get muddled near Snape. It could be a way to explore the characters' relationship in a unique way.
Well, often in these fanfictions, the marriage law forces Snape and Hermione together. Hermione might be initially resistant as she has her own ideas and Snape is not exactly her ideal partner. But as they start to live together under this new law, they begin to understand each other better. For example, Snape could see Hermione's academic passion in a new light and Hermione might come to understand Snape's past traumas that made him so cold. And the concept of having a baby in such a relationship could be a way to explore how they build a family against all odds, and how they grow as individuals and as a couple.
Well, in this fanfiction, it might start with Snape finding Hermione as a baby in a dangerous place like the Forbidden Forest. He adopts her because he sees her potential even as a baby. As she grows, he teaches her magic in his own strict way, but also forms a deep bond with her. This could lead to some interesting interactions with other Hogwarts faculty who are surprised by Snape's new role as a father figure.
She could meet other outcasts from the wizarding world. There might be witches and wizards who have left Hogwarts for similar reasons and they form a sort of community in hiding. Maybe she'll meet a powerful but reclusive wizard who can teach her things that Hogwarts never could.
In fanfiction, this could be a really interesting development. It might start with Hermione seeing a different side of Snape, perhaps his hidden kindness or his complex past that makes her view him in a new light. It could also be due to some shared experiences within the fictional scenarios created by the fanfic writer.
Snape would become more nurturing. He's used to being cold and distant, but with a baby to care for, he'd have to soften. For example, he'd learn to comfort Hermione when she cries.
She could meet the founders of Hogwarts. Imagine Hermione having a conversation with Rowena Ravenclaw about the importance of knowledge and wisdom. She might also meet Godric Gryffindor and learn about the true meaning of courage from him. Another person she could meet is Salazar Slytherin. It would be very interesting to see how she would interact with him, given his views on blood purity.
In this fanfiction, the baby's life would be full of unique experiences. Since Hermione is well - versed in many areas of magic, the baby would have an excellent education from home. Snape, being a strict father figure, would ensure the baby has a strong sense of discipline in magic. However, the baby would also face the pressure of living up to the legacies of both parents. It might feel the need to prove itself in potions like Snape and in academic studies like Hermione. Also, the family might be shunned by some in the wizarding community who can't accept their relationship, which would add to the baby's hardships.