Goku being born with SSJ4 in fanfic would likely make him a force to be reckoned with from infancy. This could result in quicker power-ups, different battles, and maybe even a shift in the balance of power among the characters.
One possible plot could be Goku from the SSJ4 form crossing over into the world of Dragon Ball GT. He could encounter new threats that require his ultimate form to defeat. Maybe he teams up with the other Z - fighters in that universe to face off against a powerful and ancient evil that was sealed away long ago and has now been unleashed.
In Dragon Ball fanfic, Goku SSJ often has super strength, like being able to lift extremely heavy objects with ease. He can also move at incredible speeds, making it hard for enemies to even see him coming. His energy blasts are much more powerful than in his normal form, capable of destroying large structures or powerful foes in one shot.
The plot might involve Goku SSJ4 teaming up with some unexpected allies in the Tournament of Power. He could be using his SSJ4 powers in creative ways, like combining them with the techniques of his new allies to gain an edge over the other universes' competitors.
Well, if they were brothers in a fanfic, it could change how they interact with the other characters. Maybe they'd have a deeper understanding and fewer power struggles between them. Also, their family background and upbringing could be explored in new and interesting ways.
One common theme is power exploration. Writers often explore the full extent of Goku's SSJ4 power in Dragon Ball Super scenarios. Another is the idea of new battles. Fans like to imagine Goku in SSJ4 facing off against different villains. Also, friendship and family themes are common, like how Goku's new power affects his relationships with his friends and family.
One scenario could be that Goku surprises Beerus with his speed and initial attacks as SSJ4. But then Beerus counters with his hakai and forces Goku to dodge constantly. Another could be that Beerus underestimates Goku at first and Goku manages to land some powerful blows.
Bulma could be involved. Since she has a relationship with Vegeta and is friends with Goku, she might try to mediate between them when Goku snaps at Vegeta. She could be the voice of reason, trying to calm both of them down and make them see each other's point of view.
Many Goku and Vegeta fanfictions explore the concept of power. How they strive for more power, what they are willing to sacrifice for it, and how they handle having great power. This can lead to some interesting moral and ethical dilemmas within the stories.