  We consider a non-singular origin for the Universe starting from an Einstein
static Universe, the so called "emergent universe" scenario, in the framework
of a theory which uses two volume elements $\sqrt{-{g}}d^{4}x$ and $\Phi
d^{4}x$, where $\Phi $ is a metric independent density, used as an additional
measure of integration. Also curvature, curvature square terms and for scale
invariance a dilaton field $\phi$ are considered in the action. The first order
formalism is applied. The integration of the equations of motion associated
with the new measure gives rise to the spontaneous symmetry breaking (S.S.B) of
scale invariance (S.I.). After S.S.B. of S.I., it is found that a non trivial
potential for the dilaton is generated. In the Einstein frame we also add a
cosmological term that parametrizes the zero point fluctuations. The resulting
effective potential for the dilaton contains two flat regions, for $\phi
\rightarrow \infty$ relevant for the non singular origin of the Universe,
followed by an inflationary phase and $\phi \rightarrow -\infty$, describing
our present Universe. The dynamics of the scalar field becomes non linear and
these non linearities produce a non trivial vacuum structure for the theory and
are responsible for the stability of some of the emergent universe solutions,
which exists for a parameter range of values of the vacuum energy in $\phi
\rightarrow -\infty$, which must be positive but not very big, avoiding the
extreme fine tuning required to keep the vacuum energy density of the present
universe small. The non trivial vacuum structure is crucial to ensure the
smooth transition from the emerging phase, to an inflationary phase and finally
to the slowly accelerated universe now. Zero vacuum energy density for the
present universe defines the threshold for the creation of the universe.
