  We study the quantum cosmology of a five dimensional non-compactified
Kaluza-Klein theory where the 4D metric depends on the fifth coordinate,
$x^4\equiv l$. This model is effectively equivalent to a 4D non-minimally
coupled dilaton field in addition to matter generated on hypersurfaces
l=constant by the extra coordinate dependence in the four-dimensional metric.
We show that the Vilenkin wave function of the universe is more convenient for
this model as it predicts a new-born 4D universe on the $l\simeq0$ constant
hypersurface.
