Often, Kid Goku is portrayed as the carefree and adventurous type. He's always looking for the next exciting thing to do, whether it's chasing after a strange animal or exploring a new area. He might be a bit naive in some aspects, especially when it comes to things like emotions.
One popular storyline could be their adventures together in the mountains. They might encounter strange creatures and have to use their wits and skills to overcome difficulties. For example, they could find a lost magical item and have to return it to its rightful place.
In the fanfiction, perhaps Kid Goku is on a journey to find stronger opponents to train with. He comes across Gine who is in a difficult situation, like being chased by some bad guys. Goku jumps in to save her. After that, Gine is so grateful that she decides to cook for Goku. As they sit down to eat, they start to exchange their life experiences. Goku is amazed by Gine's gentle nature, and Gine is impressed by Goku's courage and strength.
The two main characters are Kid Goku, the young and energetic Saiyan, and Gine, who is an important figure in the Saiyan world. Kid Goku is known for his love of fighting and his pure heart. Gine, on the other hand, has her own story and personality. In this fanfiction, their encounter will surely bring out different aspects of their characters as they interact with each other.
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.
Well, in many fanfictions, SSJ4 Goku is often depicted as having a chance against Beerus. SSJ4 Goku has shown incredible strength and combat skills. But Beerus has the power of a God of Destruction. His hakai ability could potentially wipe Goku out. Still, if the fanfiction is written in a way that gives Goku some new power - up or a special advantage, he could win. It really depends on the creative direction of the fanfic writer.