Quasars powered by massive black holes (BHs) with mass estimates above a billion solar masses have been identified at redshift 6 and beyond. The existence of such BHs requires almost continuous growth at the Eddington limit for their whole lifetime, of the order of one billion years. In this paper, we explore the possibility that positively skewed scale-dependent non-Gaussian primordial fluctuations may ease the assembly of massive BHs. In particular, they produce more low-mass haloes at high redshift, thus altering the production of metals and ultraviolet flux, believed to be important factors in BH formation. Additionally, a higher number of progenitors and of nearly equal-mass halo mergers would boost the mass increase provided by BH–BH mergers and merger-driven accretion. We use a set of two cosmological simulations, with either Gaussian or scale-dependent non-Gaussian primordial fluctuations to perform a proof-of-concept experiment to estimate how BH formation and growth are altered. We estimate the BH number density and the fraction of haloes where BHs form, for both simulations and for two popular scenarios of BH formation (remnants of the first generation of stars and direct collapse in the absence of metals and molecular hydrogen). We find that the fractions of haloes where BHs form are almost identical, but that non-Gaussian primordial perturbations increase the total number density of BHs for both BH formation scenarios by a factor of 2. We also evolve BHs using merger trees extracted from the simulations and find that both the mean BH mass and the number of the most massive BHs at z = 6.5 are up to twice the values expected for Gaussian primordial density fluctuations.