  In this paper we study the description of the Universe based on the low
energy superstring theory modified by the Loop Quantum Gravity effects.This
approach was proposed by De Risi et al. in the Phys. Rev. D {\bf 76} (2007)
103531. We show that in the contrast with the string motivated pre-Big Bang
scenario, the cosmological realisation of the $t$-duality transformation is not
necessary to avoid an initial singularity. In the model considered the universe
starts its evolution in the vacuum phase at time $t\to - \infty$. In this phase
the scale factor $a\to 0$, energy density $\rho \to 0$ and coupling of the
interactions $g^2_s \to 0$. After this stage the universe evolves to the
non-singular hot Big Bang phase $\rho \to \rho_{\text{max}} < \infty$. Then the
standard classical universe emerges. During the whole evolution the scale
factor increases monotonically. We solve this model analytically. We also
propose and solve numerically the model with an additional dilaton potential in
which the universe starts the evolution from the asymptotically free vacuum
phase $g^2_s \to 0$ and then evolves non-singularly to the emerging dark energy
dominated phase with the saturated coupling constant $g^2_s \to \text{const}$.
