  We have performed a cosmological numerical simulation of primordial baryonic
gas collapsing onto a $3\times10^7$M$_{\odot}$ dark matter (DM) halo. We show
that the large scale baryonic accretion process and the merger of few
$\sim10^6$ M$_{\odot}$ DM halos, triggered by the gravitational potential of
the biggest halo, is enough to create super sonic ($\mathcal{M}>10$) shocks and
develop a turbulent environment. In this scenario the post shocked regions are
able to produced both H$_2$ and HD molecules very efficiently reaching maximum
abundances of $n_\mathrm{H_2}\sim10^{-2}n_\mathrm{H}$ and $n_\mathrm{HD}\sim
\mathrm{few}\times10^{-6}n_\mathrm{H}$, enough to cool the gas below 100K in
some regions. The kinetic energy spectrum of the turbulent primordial gas is
close to a Burgers spectrum, $\hat{E}_k\propto k^{-2}$, which could favor the
formation of low mass primordial stars. The solenoidal to total kinetic energy
ratio is $0.65\la R_k\la0.7$ for a wide range of wave numbers; this value is
close to $R_k\approx 2/3$ natural equipartition energy value of a random
turbulent flow. In this way turbulence and molecular cooling seem to work
together in order to produce potential star formation regions of cold and dense
gas in primordial environments. We conclude that both the mergers and the
collapse process onto the main DM halo provide enough energy to develop super
sonic turbulence which favor the molecular coolants formation: this mechanism,
which could be universal and the main route toward formation of the first
galaxies, is able to create potential star forming regions at high redshift.
