ABSTRACT We introduce a suite of cosmological volume simulations to study the evolution of galaxies as part of the Feedback in Realistic Environments project. FIREbox, the principal simulation of the present suite, provides a representative sample of galaxies (∼1000 galaxies with $M_{\rm star}\gt 10^8\, M_⊙$ at z = 0) at a resolution ($Δ {}x∼ {}20\, {\rm pc}$ , $m_{\rm b}∼ {}6\times {}10^4\, M_⊙$ ) comparable to state-of-the-art galaxy zoom-in simulations. FIREbox captures the multiphase nature of the interstellar medium in a fully cosmological setting (L = 22.1 Mpc) thanks to its exceptionally high dynamic range (≳106) and the inclusion of multichannel stellar feedback. Here, we focus on validating the simulation predictions by comparing to observational data. We find that star formation rates, gas masses, and metallicities of simulated galaxies with $M_{\rm star}\lt 10^{10.5-11}\, M_⊙$ broadly agree with observations. These galaxy scaling relations extend to low masses ($M_{\rm star}∼ {}10^7\, M_⊙$ ) and follow a (broken) power-law relationship. Also reproduced are the evolution of the cosmic HI density and the HI column density distribution at z ∼ 0–5. At low z , FIREbox predicts a peak in the stellar-mass–halo-mass relation but also a higher abundance of massive galaxies and a higher cosmic star formation rate density than observed, showing that stellar feedback alone is insufficient to reproduce the properties of massive galaxies at late times. Given its high resolution and sample size, FIREbox offers a baseline prediction of galaxy formation theory in a ΛCDM Universe while also highlighting modelling challenges to be addressed in next-generation galaxy simulations.