glutShowWindow man page
glutShowWindow — Request that the <i>current window</i> be visible
OpenGLUT - window
glutShowWindow() requests that the window system make the
This is generally not necessary. When you create a window, it will normally become visible. Unless you specifically hide it, it will remain visible. Though visible, of course, it may be covered by other windows; that would be an issue for window stacking order not visibility.
When, and if, your window's visibility status changes, you may find out via a glutWindowStatusFunc() callback.
glutHideWindow(3) glutPopWindow(3) glutPushWindow(3) glutWindowStatusFunc(3)