  The presence of evolved stars in high-redshift galaxies can place valuable
indirect constraints on the onset of star formation in the Universe. Thus we
use PEARLS GTO and public NIRCam photometric data to search for Balmer-break
candidate galaxies at $7 < z < 12$. We find that our Balmer-break candidates at
$z \sim 10.5$ tend to be older (115 Myr), have lower inferred [O III] +
H$\beta$ emission line equivalent widths (120 \r{A}), have lower specific star
formation rates (6 Gyr$^{-1}$) and redder UV slopes ($\beta = -1.8$) than our
control sample of galaxies. However, these trends all become less strong at $z
\sim 8$, where the F444W filter now probes the strong rest-frame optical
emission lines, thus providing additional constraints on the current star
formation activity of these galaxies. Indeed, the bursty nature of Epoch of
Reionisation galaxies can lead to a disconnect between their current SED
profiles and their more extended star-formation histories. We discuss how
strong emission lines, the cumulative effect of weak emission lines, dusty
continua and AGN can all contribute to the photometric excess seen in the
rest-frame optical, thus mimicking the signature of a Balmer break. Additional
medium-band imaging will thus be essential to more robustly identify
Balmer-break galaxies. However, the Balmer break alone cannot serve as a
definitive proxy for the stellar age of galaxies, being complexly dependent on
the star-formation history. Ultimately, deep NIRSpec continuum spectroscopy and
MIRI imaging will provide the strongest indirect constraints on the formation
era of the first galaxies in the Universe, thereby revealing when cosmic dawn
breaks.
