Tseliakhovich and Hirata recently discovered that higher order corrections to the cosmological linear-perturbation theory lead to supersonic coherent baryonic flows just after recombination (i.e. z ≈ 1020), with rms velocities of ∼30 km s−1 relative to the underlying dark matter distribution, on comoving scales of ≲3 Mpc h−1. To study the impact of these coherent flows, we performed high-resolution N-body plus smoothed particle hydrodynamic simulations in boxes of 5.0 and 0.7 Mpc h−1, for bulk-flow velocities of 0 (as reference), 30 and 60 km s−1. The simulations follow the evolution of cosmic structures by taking into account detailed, primordial, non-equilibrium gas chemistry (i.e. H, He, H2, HD, HeH, etc.), cooling, star formation and feedback effects from stellar evolution. We find that these bulk flows suppress star formation in low-mass haloes (i.e. Mvir≲ 108 M⊙ until z ∼ 13), lower the abundance of the first objects by ∼1–20 per cent and as a consequence delay cosmic star formation history by ∼2 × 107 yr. The gas fractions in individual objects can change by up to a factor of 2 at very early times. Coherent bulk flow therefore has implications for (i) the star formation in the lowest-mass haloes (e.g. dSphs); (ii) the start of reionization by suppressing it in some patches of the Universe; and (iii) the heating (i.e. spin temperature) of neutral hydrogen. We speculate that the patchy nature of reionization and heating on several Mpc scales could lead to enhanced differences in the H i spin temperature, giving rise to stronger variations in the H i brightness temperatures during the late dark ages.