You don't want to plot data points. So tools like plot, line, scatter, etc., are all inappropriate. You don't want to plot a surface, or any function at all. So tools like surf, contour, etc., are all useless.
You are asking to plot an infinite, unbounded region. So tools like patch, that can plot anything that can be represented as a set of patches is invalid.
The point is, x>=0, y>=0, z>=0 is unbounded. Infinity is a long way out. Are your eyes good enough to see that far? You can create a cube, for example, that extends to some extent in x,y,z. Create each facet of the cube as a patch, then use patch. Or you can download the plotregion tool, found on the file exchange.
Plotting a more general region like the one you describe could be done by approximating the curved surface using a triangulation. Then you can use tools like trisurf, or just patch.