Cannot fit in the new rain shower head
Your photo is not all that helpful but it appears that you are attempting to screw the new unit into a part off of the old one.  You should remove that part that is sticking out from the disk and get to the standard plumbing stub that is coming out of the wall.  That is where your new shower head should attach.

I have no idea what that circular plate is doing.  Is it a part of the new one or the old one?  Some better photos of what you received from Amazon might help here.