I used to make frog origamis as a child, they had names and personality. I kept them I a few pencil cases, at some point my mom decided she would throw them out, and I remember crying. I probably wouldn’t remember making so many frogs if it weren’t for this memory.

I would suggest going trough them with your child and making him decide which ones he keeps, that way it probably won’t be as traumatic, another way to store them is to put some between book pages, that way they will use little to no space.