How to create a hole on 3D model , which have the shape of the 3D model dragged through the surface ,using ExtrudeGeometry?

I am trying to generate an empty hole on the side of my 3D model while dragging a 3D shape through the model .The shape of the empty hole must be the shape of the 3D model dragged through the surface. I am trying to use ExtrudeGeometry .

Maybe a library like any of the following will help to subtract one mesh from the other:

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