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 ~ 16, only 250 million years after the big bang. We also identify two candidates at z ~ 12 and six candidates at z ~ 9-11. Our search extended out to z ≲ 21 by combining colour information across seven near-infrared camera and near-infrared imager and slitless spectrograph filters. By modelling the Spectral Energy Distributions (SEDs) with EAZY and BEAGLE, we test the robustness of the photometric redshift estimates. While their intrinsic (unlensed) 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 ultraviolet-continuum slopes -3 < β < -2.4, young ages ~10-100 Myr, and stellar masses around log (M_⋆/M_⊙) = 8.8 inferred from their spectral energy distribution modelling, 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.