Traveling gives them a chance to be away from the normal distractions of their home. They can have long conversations while on the road or during breaks. Sasuke could share his dreams of a peaceful future for the ninja world, and Sakura could talk about her hopes for the medical advancements in their village. As they communicate more, they start to understand each other better. And as they face difficulties together, like bad weather or bandit attacks, they rely on each other more, which gradually turns into a deeper love.
If they travel to a time where they are younger versions of themselves, they could have a chance to start their relationship from a different perspective. They could become friends in a more natural way without all the baggage from their original timeline. As they grow up again in this new time, their relationship would be based on a deeper understanding and shared experiences, which would make it a more healthy and loving relationship compared to what they had originally.
Well, during time travel, they might face situations that test their relationship. If they travel to a time when Sasuke's family was still alive, Sakura could get to know a different side of Sasuke. This new understanding could make their relationship more complex and intimate. They would share experiences that are unique to just the two of them, which would bring them closer together in a different way than in their original timeline.
At first, Sasuke might start with small gestures. For instance, he could be more attentive to Sakura's presence, like looking at her more often or listening more closely when she speaks. This could gradually lead to more direct interactions, such as him starting conversations with her instead of the other way around.
The relationship can start with a moment of vulnerability. For example, if Sakura is in a dangerous situation and Sasuke comes to her rescue. His licking of her (in a non - sexual, affectionate way like licking a wound) can be the first sign of his deeper care for her. This could lead to Sakura realizing that Sasuke's feelings for her have changed, and she starts to open up more to him.
The relationship could start with mutual respect. Since they know each other from before, they have a basic understanding. Then, small acts of kindness from Sakura towards Sasuke, like cooking his favorite food or patching up his wounds, could start to break down Sasuke's walls. Eventually, they might share a moment of vulnerability, like Sasuke opening up about his past traumas, which would bring them closer.
As Sakura teaches Sasuke, they could start to understand each other on a more personal level. They might share their dreams and fears, which would bring them closer. Eventually, they could develop romantic feelings for each other as they realize how much they have in common and how well they complement each other.
During their travels, they would have to depend on each other. Sasuke might protect Sakura from physical threats, and Sakura would take care of Sasuke when he's injured. This mutual reliance would bring them closer. They'd also have time to talk about their dreams and fears, which would further develop their relationship into a more loving and trusting one.
In some fanfiction, the secret relationship develops as a result of a common goal. They both want to change the ninja world in some way. Working towards this goal together, they find themselves relying on each other more and more. They start to communicate on a deeper level, and this leads to romantic feelings. However, they keep it hidden because they know that their relationship could be a distraction to their comrades or a target for their enemies. They have to be careful, so they only show their true relationship when they are completely alone.
Often in fanfiction, the relationship develops as they train together. They learn new skills from each other. Naruto teaches Sasuke about the power of friendship and determination, Sasuke shows Naruto and Sakura some advanced Uchiha techniques. Sakura, with her medical knowledge, helps them both when they get injured during training. This mutual learning and support strengthen their bond.
The relationship could start with Sasuke being secretly jealous of Sakura's closeness to someone else. He might not show it at first, but little actions would give it away. For instance, he might glare at the other person when they are around Sakura. Sakura, being perceptive, could start to suspect something. This would create an interesting dynamic as she tries to figure out what's wrong with Sasuke.