  We introduce SERRA, a suite of zoom-in high-resolution ($\sim 10\,\rm pc$)
cosmological simulations including non-equilibrium chemistry and on-the-fly
radiative transfer. The outputs are post-processed to derive galaxy UV+FIR
continuum and emission line properties. Results are compared with available
multi-wavelength data to constrain the physical properties (e.g., star
formation rates, stellar/gas/dust mass, metallicity) of high-redshift $6
\lesssim z \lesssim 15$ galaxies. This flagship paper focuses on the $z=7.7$
sub-sample, including 202 galaxies with stellar mass $10^7 M_\odot \lesssim
M_\star \lesssim 5\times 10^{10}M_\odot$, and specific star formation ranging
from ${\rm sSFR} \sim 100\,{\rm Gyr}^{-1}$ in young, low-mass galaxies to $\sim
10\,{\rm Gyr}^{-1}$ for older, massive ones. At this redshift, SERRA galaxies
are typically bursty, i.e. they are located above the Schmidt-Kennicutt
relation by a factor $\kappa_s = 3.03^{+4.9}_{-1.8}$, consistent with recent
findings for [OIII] and [CII] emitters at high-$z$. They also show relatively
large ${\rm IRX} = L_{\rm FIR}/L_{\rm UV}$ values as a result of their
compact/clumpy morphology effectively blocking the stellar UV luminosity. Note
that this conclusion might be affected by insufficient spatial resolution at
the molecular cloud level. We confirm that early galaxies lie on the standard
$\rm [CII]-SFR$ relation; their observed $L_{\rm [OIII]}/L_{\rm [CII]} \simeq
1-10$ ratios can be reproduced by a part of the SERRA galaxies without the need
of a top-heavy IMF and/or anomalous C/O abundances. [OI] line intensities are
similar to local ones, making ALMA high-$z$ detections challenging but feasible
($\sim 6\,\rm hr$ for a SFR of $50\,M_\odot\,{\rm yr}^{-1}$).
