Yes, there might be. There are a lot of fanfiction websites out there where fans create various stories. You can try searching on popular fanfiction platforms like Archive of Our Own or FanFiction.net. However, not all fanfictions are of high quality, so you may need to do some sifting.
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.
A common theme is training. Since Goku is a master of martial arts, many fanfictions focus on him training Caulifla, like in 'Training Days'. It could be about her learning new forms or just improving her basic skills.
One frequent theme is power - up. Given that Goku is known for his various Super Saiyan forms and Caulifla is also a strong Saiyan, fanfictions like to show them achieving new levels of power, either through training or facing a powerful foe. Additionally, the theme of respect is also common. As they witness each other's strength, they gain respect for one another, which is often depicted in these fanfictions.
Friendship and mentorship are also common. Goku is often seen as a mentor figure to Caulifla in these fanfics. They form a bond through training and fighting side by side. Another theme could be the exploration of different universes. Given that they are from different universes in the Dragon Ball series, fanfics may play around with the idea of them exploring each other's worlds and cultures.
I'm not entirely sure specifically what that particular fanfic is about as there could be many interpretations. 'Caulifla' and 'Goku' are characters from the Dragon Ball series. A fanfic might involve some kind of adventure, relationship exploration, or unique power - up scenarios between them. But without reading it, it's hard to say for certain.
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.