so it seems you have the object modeled. You may have it “outside” of the piece component. You may need to put it inside the component so that the hole edges can interact with the piece surface, and you can therefore erase the face in the oval and see inside.
Give it a try. Since you downloaded it, no telling if it was done properly and if it will lie on the face correctly.
You will eventually make your own holes: just make the cylindrical shape that the drill makes, intersect faces with your piece and delete the parts that you don’t need. And you’ll pick up steps to make it easier. Even easier than opening the 3DWH