This study investigates the electronic band structure of chromium sulfur bromide (CrSBr) through comprehensive photoluminescence (PL) characterization. We clearly identify low-temperature optical transitions between two closely adjacent conduction-band states and two different valence-band states. The analysis on the PL data robustly unveils energy splittings, band gaps, and excitonic transitions across different thicknesses of CrSBr, from monolayer to bulk. Temperature-dependent PL measurements elucidate the stability of the band splitting below the Néel temperature, suggesting that magnons coupled with excitons are responsible for the symmetry breaking and brightening of the transitions from the secondary conduction band minimum (CBM2) to the global valence band maximum (VBM1). Collectively, these results not only reveal splitting in both the conduction and valence bands but also highlight a significant advance in our understanding of the interplay between the optical, electronic, and magnetic properties of antiferromagnetic two-dimensional van der Waals crystals.