One possible plot could be that Naruto feels constantly overshadowed by his family's expectations. Maybe his family is full of powerful shinobi and they expect him to be just as great immediately. He runs away to find his own path and prove himself on his own terms. Along the way, he meets new friends who are also outcasts and together they form a sort of 'family' that accepts him for who he is.
It could be that Naruto's family is too overprotective. They don't let him take any risks or go on adventures. Feeling stifled, he runs away. He then embarks on a journey across the shinobi world. During this journey, he encounters various challenges that test his skills and character. He learns a lot about himself and the world, and realizes that he can be his own person, independent of his family's influence.
It might be that his family is overprotective. Naruto is a very independent character. If his family in the fanfiction is constantly trying to hold him back from taking risks or going on adventures, he may feel suffocated. Running away would be his way of breaking free and exploring the world on his own terms.
The family would be shocked at first. They might start to question their actions towards Naruto. If they were too strict or didn't give him enough love, they would feel guilty. For example, his father may realize that he pushed Naruto too hard to follow a certain path and now regrets it.
He might meet an old hermit who teaches him a unique and powerful jutsu that his family never knew. This new jutsu gives him an edge and also makes him more confident in his abilities. He could then use this newfound power to help those in need, all while staying away from his family.
Maybe he feels misunderstood by his family. In many Naruto stories, his family situation can be complex. If he's 'godlike', he might have powers that his family doesn't understand or fears, leading him to run away to avoid conflict or being treated differently.
Running away from his family can make Naruto more independent. He has to rely on himself, which would strengthen his self - reliance. He'll learn to make decisions without the influence of his family, and this could make him a more decisive ninja.
One possible reason could be that he feels misunderstood. In the Naruto series, Naruto often faced isolation and judgment from the villagers. If this extended to his family in the fanfiction, he might run away to find a place where he is accepted. Maybe he discovers some dark secrets about his family that make him feel unsafe or betrayed.
Naruto might rely on his ninja skills that he's learned. He's a resourceful character, so he'd use his stealth and combat abilities to find food and shelter. For instance, he could hunt small animals in the forest and build a simple shelter using his knowledge of basic survival techniques.
He could become stronger on his own. Away from his family, he'll have to rely solely on himself. This self - reliance might push him to train harder and unlock even more of his 'godlike' powers. For instance, he might find new mentors or training methods that his family would not have allowed.
He could be running away because of false accusations within the family. Just like how he was wrongly judged by the village in the original story, if his family wrongly blames him for something he didn't do, like stealing a family heirloom or causing harm to a family member accidentally, he might choose to run away rather than face their unjust wrath.
Sakura would be very worried. She has always cared about Naruto, even if she sometimes gets annoyed with his antics. She would probably try to find him right away, thinking that he's in some kind of trouble.