How do you cast shadows on moveable objects like these?

Every object is moveable. How do you cast shadows on moveable objects like these?

The reason they need to be movable is because we have a command that changes colors and separate object into pieces. Therefore, it’s unavoidable to use mesh as moveable.

Is there any solutions to this?

Ambient occlusion can produce those shadows: Ambient Occlusion | Unreal Engine Documentation