Cosmological hydrodynamical simulations have become an important theoretical tool for understanding the formation and evolution of the first galaxies during cosmic dawn, between redshifts 5 and 15. I will introduce the FirstLight database of about 300 zoom-in simulations with a resolution of 10 parsecs. This database agrees well with observed UV luminosity functions and stellar mass functions. I will discuss the origin and evolution of the star-forming main sequence of galaxies and the main drivers of the star formation histories at these early epochs. I will show simulated SEDs from UV to IR, including stellar and nebular emission. The rest-frame UV spectra show steep slopes and a high production efficiency of Lyman continuum photons. These properties are consistent with young stellar populations with low metallicities. Simulated recombination lines allow us to link the physical conditions of the gas around these stellar populations with observables, like equivalent widths in OIII or Hα or BPT diagrams at high-z. These simulations are making predictions that will be tested for the first time in future deep fields with the James Webb Space Telescope (JWST). I will finally discuss preliminary results involving JWST mock fields and predictions for ALMA observations by post-processing FirstLight snapshots with Powderday radiative transfer code.