We identify a physical mechanism that would have resulted in rapid, obscured growth of seed supermassive black holes in galaxies at z≳6. Specifically, we find that the density at the centre of typical high-redshift galaxies was at a level where the Bondi accretion rate implies a diffusion speed of photons that was slower than the gravitational infall velocity, resulting in photons being trapped within the accretion flow and advected into the black hole. We show that there is a range of black hole masses (Mbh ∼ 103 − 5 M⊙) where the accretion flow traps radiation, corresponding to black holes that were massive enough to generate a photon trapping accretion flow, but small enough that their Bondi radii did not exceed the isothermal scale height of self-gravitating gas. Under these conditions we find that the accretion reaches levels far in excess of the Eddington rate. A prediction of this scenario is that X-ray number counts of active galactic nuclei at z≳6 would exhibit a cutoff at the low luminosities corresponding to black hole masses below ∼105 M⊙. The super-Eddington growth of ∼105 M⊙ seed black holes at high redshift may have provided a natural acceleration towards the growth of supermassive black holes at , less than a billion years after the big bang.