  We apply quantum cosmology to investigate the early moments of a
Friedmann-Lema\^itre-Robertson-Walker (FLRW) cosmological model, using
Ho\v{r}ava-Lifshitz (HL) as the gravitational theory. The matter content of the
model is a dust perfect fluid. We start studying the classical model. Then, we
write the total Hamiltonian of the model, quantize it and find the appropriate
Wheeler-DeWitt equation. In order to avoid factor ordering ambiguities, in the
Wheeler-DeWitt equation, we introduce a canonical transformation. We solve that
equation using the Wentzel-Kramers-Brillouin (WKB) approximation and compute
the tunneling probabilities for the birth of that universe ($TP_{WKB}$). Since
the WKB wavefunction depends on the dust energy and the free coupling constants
coming from the HL theory, we compute the behavior of $TP_{WKB}$ as a function
of all these quantities.
