SSDs are usually half the thickness of the original HDDs, so if you try to install one horizontally, it can sag into the leftover space making it difficult to get the heads of side screws to fit into their “sockets” against the front of the case.
solution:
stand the MacMini on its “nose.” Now the SSD can be installed “vertically” and it’s easier to get the side screw heads to fit into their places at the front of the case.