In a fanfiction about baby Naruto's birth, a really interesting aspect could be the secrets that were passed down during that time. For example, if there were any special Uzumaki clan traditions related to the birth of a new heir. And what if some of the older ninja in the village, who knew about the Uzumaki clan's power, were already making plans for Naruto's future? Maybe they were thinking about how to train him to be a great asset to the village from the very start.
One interesting plot could be baby Naruto and baby Sasuke getting lost in the forest together. They have to rely on their budding instincts and nascent chakra to find their way back. Maybe they encounter some small, friendly forest creatures that help them. Another idea is that they accidentally switch places in the village for a day. This leads to chaos as the villagers react differently to them being in the wrong 'homes'.
One idea could be exploring the circumstances of his birth from the perspective of his mother. Maybe she had a premonition about Naruto's future as a great ninja. Another could be how Minato, his father, prepared for his arrival during the chaos of the war-torn era. Also, a fanfiction could focus on the secrecy surrounding his birth due to the Nine - Tails being sealed within him, and how that affected the village's initial reaction to his birth.
Another idea is that baby Sasuke and Naruto are found together by a third party, like a wandering ninja who decides to train them both from a very young age. This would create a different dynamic as they grow up together with a unique set of skills taught by this unknown mentor. They would probably have a stronger bond from the start compared to in the original story.
Well, a plot could be that baby Naruto's presence starts to have an unexpected effect on Kyuubi. Kyuubi, who was once full of hatred, begins to feel a strange sense of attachment to the baby. As a result, Kyuubi starts to share some of its chakra with Naruto in a very small and controlled way, which gives Naruto some unique abilities even as a baby. And there could be a plot where other shinobi sense this strange chakra and start to investigate Naruto.
One idea could be Itachi discovers Baby Naruto has a unique chakra signature that could change the future of the ninja world. So, he decides to secretly protect Naruto from afar. Another could be Itachi is tasked with a mission that involves Baby Naruto in some way, like having to test Naruto's potential without the village knowing. And a third could be Itachi has a vision of a future where Baby Naruto is the key to peace, and he starts to subtly influence Naruto's growth even at that young age.
Perhaps in the fanfiction, the baby nine - tails gets separated from Naruto for a while. During this time, it has to fend for itself in a world that fears it. It could meet other friendly or hostile creatures and have various adventures before reuniting with Naruto.
A possible plot is that Boruto discovers a hidden power within himself that was passed down from Naruto and Hinata combined. This power could put him in a dangerous situation as various factions might want to either control or eliminate him. Or perhaps Boruto has to deal with the pressure of being the son of the Hokage and a powerful Hyuga, and he decides to go on a journey to find his own identity away from his parents' shadows.
Perhaps the fanfiction could revolve around the challenges during the birth. There could be some complications, but through the love and support of the family and the skills of the medical staff, baby Shikadai is born safely. It could also show how the community around them comes together to support the new family during this time.
One idea could be exploring the emotions of Hinata during the birth. Maybe she's worried about Boruto's future in a world filled with challenges. Another could be how Naruto, as a new father, is torn between his duties as Hokage and being there for his family. For example, he might have to leave Hinata's side during the birth to deal with a sudden threat to the village, and then rush back to be with his new - born son.
One idea could be that baby Naruto somehow crosses paths with Itachi in a secret mission. Maybe Itachi is on a mission in Konoha and stumbles upon baby Naruto who has an unusual chakra flare. Itachi, being curious, decides to keep an eye on him without revealing himself. This could lead to a series of events where Itachi's actions unknowingly protect Naruto from some early threats.