Hi.
It is entirely possible that I have misinterpreted your question, but here goes:
In Sketchup, the default workspace vaguely emulates a real world environment, where the ground plane at the bottom of the screen is the X(red) Y(green) plane. The Z(blue) direction is vertical.
If you wish to orient all of your modelling along the z axis, the most likely thing to do is to use the Views toolbar. Go to top line menu View> Toolbars> In the flyout menu select Views. These are orthogonal camera positions Isometric view, Top, Front, Right, Back, Left. The toolbar appears and the icons are depicted as views of a house. If you select Top, you will be viewing along the Sketchup Z axis.
Alternatively, if you do not want to set a toolbar, you can go to Camera> Standard Views> and the flyout is a list of the same views to select.
Sketchup's mode of operation is geared toward the default workspace world environment. It may be that you have selected a template that does not provide visual cues for orienting your work. Go to Window> Preferences> Template and select in the box your preferred working environment. I have always used Simple Template, but you could select from quite a few there.
I am hoping some of this helps you. If not, reply back for more information.