I know how to do.
1. Go to CAS, then save your household to your library.
2. Go back to Main menu, then click '+' icon on top right and start a new CAS.
3. There will be a random sim in CAS. Just open the library in CAS, then you will see your saved family on right side of your library.
4. Download the family and it will ask 'merge' or 'replace'. Select 'Replace', then the random sim will be gone and only your family will be left in CAS.
5. And then, just click 'ok'. then you can start a NEW Fresh game with your saved family.
If you start a new game with your saved family, then they will lose all money, the records of all collections, all relationships except for the family tree, and home lot. The Sims 4 doesn't allow to save the family with home lot. Only Sim Family can be saved, and you need to save your home lot separately.
For me, I moved my current family into the new game, I got the exact money my family had in the previous game by money cheat, then, I placed the saved home lot in the new game, then let them move back in the home lot with freerealestate cheat.
And the rest of their specs like job, aspirations and skills are all safe.
--- When the household is saved to the library and/or gallery they loose all family and individual inventory.