  One of the main goals of the JWST is to study the first galaxies in the
Universe. We present a systematic photometric analysis of very distant galaxies
in the first JWST deep field towards the massive lensing cluster SMACS0723. As
a result, we report the discovery of two galaxy candidates at $z\sim16$, only
$250$ million years after the Big Bang. We also identify two candidates at
$z\sim 12$ and 6 candidates at $z\sim 9-11$. Our search extended out to
$z\lesssim21$ by combining color information across seven NIRCam and NIRISS
filters. By modelling the Spectral Energy Distributions (SEDs) with
\texttt{EAZY} and \texttt{BEAGLE}, we test the robustness of the photometric
redshift estimates. While their intrinsic (un-lensed) luminosity is typical of
the characteristic luminosity L$^*$ at $z>10$, our high-redshift galaxies
typically show small sizes and their morphologies are consistent with disks in
some cases. The highest-redshift candidates have extremely blue UV-continuum
slopes $-3 < \beta <-2.4$, young ages $\sim 10-100$\,Myr, and stellar masses
around $\log(M_{\star}/\mathrm{M}_{\odot})=8.8$ inferred from their SED
modeling, which indicate a rapid build-up of their stellar mass. Our search
clearly demonstrates the capabilities of JWST to uncover robust photometric
candidates up to very high redshifts, and peer into the formation epoch of the
first galaxies.
