The wave description is an approximation to whatever the underlying reality is, and it only applies in some circumstances. I'm sure you heard of wave/particle duality i.e. the fact that objects behave as waves in some circumstances and particles in others. This means that while the wave description can be an excellent description in some circumstances it is a very poor description in others.
In particular once the wavelength approaches the physical size of the object we cannot usefully treat the object as a single wave. Once the wavelength, and hence the resolution, of the wave falls below the size of the object its components will start behaving independantly. So for example, once the de Broglie wavelength of a proton falls below its size we need to treat it as a collection of partons not a single object.
This means you could only assign a wavelength to the universe if its wavelength was (considerably) bigger than the universe, which is obviously impossible.