We have performed a cosmological numerical simulation of primordial baryonic gas collapsing on to a 3 × 107 M⊙ dark matter (DM) halo. We show that the large scale baryonic accretion process and the merger of few ∼ 106 M⊙ DM haloes, triggered by the gravitational potential of the biggest halo, are enough to create supersonic () shocks and develop a turbulent environment. In this scenario, the post-shocked regions are able to produce both H2 and deuterated H2 molecules very efficiently, reaching maximum abundances of and nHD∼ few × 10−6 nH, enough to cool the gas below 100 K in some regions. The kinetic energy spectrum of the turbulent primordial gas is close to a Burgers spectrum, , which could favour the formation of low-mass primordial stars. The solenoidal-to-total kinetic energy ratio is 0.65 ≲Rk≲ 0.7 for a wide range of wavenumbers; this value is close to the Rk≈ 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 dense gas in primordial environments. We conclude that both the mergers and the collapse process on to the main DM halo provide enough energy to develop supersonic turbulence which favours the molecular coolant formation: this mechanism, which could be universal and the main route towards the formation of the first galaxies, is able to create potential star-forming regions at high redshift.