  Active galactic nuclei (AGN) 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 AGN grew to the observed high
masses already at high redshifts. Observations of high-redshift SMBH
progenitors or lower-luminosity AGN 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 AGN. We assess the observability of such low luminosity AGN,
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 $10^4 {\rm \ M}_{\odot}$, at the
center of a dark matter halo and follow their growth until $z\sim6$. 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 onto 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.
