The procedure to evaluate anything Hawking et al say is to list all of the serial assumptions which are made and which have to be “the case” in order for his theories to be valid, and then to see at which of the assumptions empirical validation automatically cease, leaving the theory to be a bed time story for physicist speculators.
This theory is no different.
OK, first off it is not the Wave Theory of the Universe, it is Wave Theory Within an Infinite Multiverse which both is external to our universe, and contains our universe.
The theory, according to Wikipedia and a couple of other sites, goes like this:
There exists an infinite number of universes, within which our universe exists and has a waveform which exists such as to predict a high probability of the existence of our universe with regard to other universes.
”The Hartle–Hawking state is the wave function of the Universe—a notion meant to figure out how the Universe started—that is calculated from Feynman's path integral.
More precisely, it is a hypothetical vector in the Hilbert space of a theory of quantum gravity that describes this wave function.
It is a functional of the metric tensor defined at a (D − 1)-dimensional compact surface, the Universe, where D is the spacetime dimension. The precise form of the Hartle–Hawking state is the path integral over all D-dimensional geometries that have the required induced metric on their boundary. According to the theory time diverged from three state dimension—as we know the time now[clarification needed]—after the universe was at the age of the Planck time.
Such a wave function of the Universe can be shown to satisfy the Wheeler–DeWitt equation." 
Wave Theory works for particles within our universe, which is a physical Hilbert space. It is an ungrounded (wild) assumption to premise that a) there is an exo-universe, or infinite possible universes, b) that the Set [all possible universes] is a physical Hilbert space, and c) that our universe has an external vector in the Set [all possible universes] Hilbert space. (Three ungrounded assumptions).
Further, how was the three dimensional space able to “age” before there was time? This could happen only if the infinite multiverse also had time in which the space coordinates could “age”. This would mean that the infinite universe has a common environment in which space and time exist even between universes. That common environment would indicate a superset, Set [all possible universes], which is infinitely large (in order to contain an infinite number of universes), AND which is both physical and temporal in nature. (Fourth ungrounded assumption).
The grounding of this necessary attribute is problematic. Did this superset, Set [all possible universes] always exist? Did it exist in the distant past? And if our universe only recently came into being, then the superset, Set [all possible universes], could not have contained “all possible” universes since it did not contain our universe. This is a logical contradiction.
Next is the issue of why our particular universe would have the dominant probability wave. The answer is that it just does, because it works as a physical universe (all the constants are in harmony). This is just a Tautology: It has to work because it does work (it works because it works). Thus, because it obviously is here, it has to have a probability of 1.0 of existing as it is.
And, if the probability wave indicates the necessity of a universe existing like ours does, why did it not always exist, within the Set [all possible universes]? Because our universe did not always exist, then the set was not complete until our universe finally existed. And if our universe has a probability of 1.0 of existing, then why did it NOT always exist? This is a logical lock-out. 
Finally, if the Set [all possible universes] is physical in the sense of being composed of space/time in order to act as a Hilbert space, then changes in space/time require causes. A unique effect requires a unique cause, and the effect cannot be greater than the cause. This leads to the age old conundrum: can a universe containing life, consciousness, intellect and agency be created from a causeless environment, and if a cause is required, then what must the characteristics of the cause be? Well the cause must be very complex.
This is especially the case, given that First Life cannot be explained by deterministic properties of minerals, and neither can independent life, consciousness and self-awareness, intellect and the ability to know and analyze, and the agency to perform non-deterministic, self-determined actions.