Observations of massive black holes (MBHs) at high redshift (greater than five) challenge our theoretical understanding of black hole seed formation and early growth. We compare JWST observations of high-z MBHs with results from large-scale cosmological simulations (TNG300, EAGLE, SIMBA) in the redshift range between five and seven, finding that theoretical predictions under (over) estimate the observed masses (accretion rates) of MBHs. We thus present a semi-numeric model, based on the Uchuu large scale N-body simulations, that allows us to compute the growth of BHs starting from different seeding and accretion prescriptions. For what concerns seeding, we consider three possible scenarios (PopIII remnants, direct collapse BHs and primordial BHs) that differ in terms of seeding epochs and seed masses. For what concerns accretion, we parametrize the Eddington ratio distribution with a redshift-dependent log-normal, including both super-Eddington accretion and an accretion-dependent radiative efficiency. We determine the free parameters of the accretion model using an MCMC algorithm and exploiting the BH masses observed by JWST in the redshift range from five to eleven. Based on our results, we finally show how JWST observations, particularly at redshifts beyond eight, will play critical role in constraining the origin and growth of the earliest MBHs.