  While JWST has observed galaxies assembling as early as $z\sim14$, evidence
of galaxies with significant old stellar populations in the Epoch of
Reionisation (EoR) -- the descendants of these earliest galaxies -- are few and
far between. Bursty star-formation histories (SFHs) have been invoked to
explain the detectability of the earliest UV-bright galaxies, but also to
interpret galaxies showing Balmer breaks without nebular emission lines. We
present the first spectroscopic evidence of a $z\sim7.9$ galaxy, A2744-YD4,
which shows a Balmer break and emission lines, indicating the presence of both
a mature and young stellar population. The spectrum of A2744-YD4 shows peculiar
emission line ratios suggesting a relatively low ionisation parameter and high
gas-phase metallicity. A median stack of galaxies with similar emission line
ratios reveals a clear Balmer break in their stacked spectrum. This suggests
that a mature stellar population ($\sim 80$ Myr old) has produced a chemically
enriched, disrupted interstellar medium. Based on SED-fitting and comparison to
simulations, we conclude that the observed young stellar population is in fact
the result of a rejuvenation event following a lull in star formation lasting
$\sim 20$ Myr, making A2744-YD4 and our stack the first spectroscopic
confirmation of galaxies that have rejuvenated following a mini-quenched phase.
These rejuvenating galaxies appear to be in an exceptional evolutionary moment
where they can be identified. Our analysis shows that a young stellar
population of just $\sim 30 \%$ of the total stellar mass would erase the
Balmer break. Hence, 'outshining' through bursty SFHs of galaxies in the early
Universe is likely plaguing attempts to measure their stellar ages and masses
accurately.
