Yes you can dig them up and pot them up. Try not to damage the stems or roots. Try to handle them by the leaves. They transplant very easily when young. When they get larger you can plant them out into your garden. I have raised a lot of Japanese maples from seed. They have turned into lovely trees. Seedlings may not look like the parent tree if from a hybrid.

I find them every year under my maple. They are adorable and I use them in my containers a lot. I have also planted some in the ground and given some away to many happy friends.

I rarely lose one; they appear to be quite sturdy. Slugs will eat them, though, and that will kill a baby tree. I would pot them up right away and protect them from slugs.