Active galactic nuclei (AGNs) in the early Universe are thought to be prominent sources of energy and ionizing photons that affected the growth of their host galaxy and their environment. However, it is still unclear how the supermassive black holes (SMBHs) that fuel these AGNs grew to the observed high masses already at high redshifts. Observations of high-redshift SMBH progenitors or lower luminosity AGNs will thus help characterize the evolution of SMBHs and their impact on the surroundings. With the launch of the JWST, fainter objects at high redshifts can now be detected, including lower luminosity AGNs. We assess the observability of such low-luminosity AGNs, using the cosmological simulation code gizmo to provide a realistic environment for black hole growth in the early Universe. Soon after the first stars are born in the simulation run, we insert stellar-remnant black hole seeds of various initial masses, between 300 and 10⁴ M_⊙, at the centre of a dark matter halo and follow their growth until z ∼ 6. Such stellar black hole seeds placed in a typical high-z environment do not significantly accrete and grow to reach masses that can be observed with the JWST under conditions of standard Bondi–Hoyle accretion, as energy input from stellar feedback and chaotic dynamics prevent efficient gas accretion on to the black holes. To be observed with the JWST, rarer but still physically feasible growth regimes, involving Eddington or super-Eddington accretion, would be required. Alternatively, AGN observability may be boosted under even rarer conditions of extreme gravitational lensing.