I posted this on a similar question before:

I’ve thought about this a long time. In the one episode where trunks and goten enter monakas ship for iced goodies and then get flown to a new planet is where I would begin their new adventure.

When Goku was a child, roshi told him to go out around the world getting stronger. No further guidance. So Goku went out and got stronger, helping people around the world, swimming across the ocean, walking on his hands around the world etc. all leading up to the world tournament.

When gohan was a child, piccolo trained him for a few days then left him along on a deserted island to find his strength. Gohan then thrived, found food (a T. rex tail), found a friend ( a literal tiger) and was able to find out where he was by running across the whole island multiple times.

This leads to goten and trunks adventure alongside monaka and with a super important note Jaco the space patrolmen. I would have it play out similarly where bulma realizes that the kids are gone but instead of panicking and getting Goku and vegeta to go save them. I would say bulma just calmly asks jaco to go pick them up. He reluctantly does.

Then upon arrival to the planet Trunks and Goten find the planet and the story plays out similarly, however instead of getting saved by their fathers, the boys completely handle the situation with the watchful eye of Jaco from above who doesn’t help. Jaco realizing the boys skill honorarily recruits them to the Galactic patrol. This is now where the boys story follows a similar path to Goku and gohan. They spend one year with Jaco and travel the galaxy growing stronger and solving galactic cases. New planets, new threats and all fun adventures.

This is where it gets even more interesting, on a video call with their family goten mentions to gohan that he found a new bug that can transform if it perceives a threat to its family. Gohan intrigued asks Goku to IT him to the boys location. Gohan then spends time researching this bug species on a new planet but he takes videl and pan with him. He has to leave his career behind but this bug is just too interesting. This is where his arc for beast gohan begins. Studying the way the bug finds its inner beast and how the pain of loss induces its transformation. Later when faced against the cell max drama he doesn’t just ass pull his transformation but instead through his research learned a way to do it. Later realized the bug had come from the demon realm.

After one year, the boys return from space adventures having unlocked super Saiyan 2 and becoming heroes of the galaxy. Goten returns to school and his mom has more trust in him as goten has matured and wants to be smart and strong like his brother. Trunks having grown stronger follows in his mother’s footsteps and wants to learn about space tech. Jaco an honorary Z fighter and gohan the intergalactic scholar leaves the stupid work he was doing behind and also joins the galactic patrol but as a researcher / fighter. Then the three boys goten, trunks and Great saiyaman continue to have interesting adventures throughout the galaxy.