  We examine the assembly process and the observability of a first galaxy
(M_vir~10^9 solar mass at z~8) with cosmological zoom-in, hydrodynamic
simulations, including the radiative, mechanical, and chemical feedback exerted
by the first generations of stars. To assess the detectability of such dwarf
systems with the upcoming James Webb Space Telescope (JWST), we construct the
spectral energy distribution for the simulated galaxy in a post-processing
fashion. We find that while the non-ionizing UV continuum emitted by the
simulated galaxy is expected to be below the JWST detection limit, the galaxy
might be detectable using its nebular emission, specifically in the H-alpha
recombination line. This requires that the galaxy experiences an active
starburst with a star formation rate of Mdot_star > 0.1 Msun/yr at z~9. Due to
the bursty nature of star formation in the first galaxies, the time interval
for strong nebular emission is short, less than 2-3 Myr. The probability of
capturing such primordial dwarf galaxies during the observable part of their
duty cycle is thus low, resulting in number densities of order one source in a
single pointing with MIRI onboard the JWST, for very deep exposures.
Gravitational lensing, however, will boost their observability beyond this
conservative baseline. The first sources of light will thus come firmly within
our reach.
