In a fanfiction where Naruto and Hinata are stuck in the past, one possibility is that they would be seen as strangers at first. Naruto's unique abilities and Hinata's gentle yet strong presence would attract attention. They could end up being involved in some of the key historical events of the ninja world in different ways. Naruto might try to change the outcome of some battles, while Hinata could use her Byakugan to uncover secrets that were lost in the original timeline. This could lead to a whole new series of events and relationships, and might even change the future they came from in unexpected ways.
They might try to change some past events. For example, Naruto could prevent some of the early tragedies in the village. Hinata might also get the chance to be more assertive earlier in her life, since she has Naruto by her side this time. They could also have an impact on the relationships between different ninja clans.
Another thing that could occur is that they encounter some strange creatures or phenomena inside the box. Naruto would be ready to fight, but Hinata might first try to understand the nature of these things. They'd have to combine their different approaches to deal with the situation, and in the process, their relationship would evolve, whether it's becoming better friends or something more romantic.
They could use their ninja skills to try and break out of the box. Naruto might try his Rasengan, while Hinata could use her Gentle Fist to find weak points in the box's structure.
Well, if Naruto and Hinata go to the past in fanfiction, it could be really interesting. They could meet their younger selves. Naruto might see his lonely childhood self and try to give him some hope. Hinata could also see her shy younger self and perhaps encourage her to be more confident earlier. And they could also influence the relationships between other characters. For instance, they might help their friends' parents get together or something like that.
Their relationship could develop more quickly. In the past, without all the distractions and responsibilities of their original time, they could focus more on each other. Hinata might be more confident in expressing her feelings earlier, and Naruto would likely be more receptive since he's away from his normal hectic life.
In this fanfiction situation, they could end up using their knowledge of the future to help people in the past. For example, Ash could use his Pokémon training skills to solve some problems that people in the past were having with wild Pokémon. Serena could perhaps use her cooking skills to introduce new recipes. And together, they would be constantly looking for clues or a magical item that could send them back to their time.
In the fanfiction, it could be that Hinata is already proficient in kenjutsu. She then teaches Naruto some of the basics. As Naruto learns, they start to have a better understanding of each other's fighting styles. This could lead to them working together more effectively in future battles and also in their relationship development.
In a fanfiction, they could be involved in a race. Naruto's speed, Sasuke's sharingan - enhanced perception, and Hinata's byakugan - aided navigation could all play a part. Maybe they start off competing against each other but then realize that there's an outside threat during the race. So they put aside their differences and work together to overcome the threat, forging a stronger bond in the process.
The fanfiction could show how their relationship deepens during the pregnancy. They could have more quiet, intimate moments together, like sitting on the porch at sunset and talking about their hopes for their child. Hinata could share her dreams of their child growing up strong and kind, like Naruto.
Well, it could be that they have a sleepover at Hinata's place. They might cook a simple meal together like ramen. And then, while sitting around, Naruto could accidentally fall asleep first. Hinata might then take a moment to watch him sleep peacefully, blushing a bit as she realizes how much she cares for him. Later, she might cover him with a blanket and quietly go to sleep herself.
They might visit the local market. Naruto would be excited about all the different foods and items, and Hinata would be happy to follow him around. They could buy some cute souvenirs or some new ninja tools for Naruto. Then they could sit at a small cafe and enjoy some tea while talking about their friends and family.