Star-forming galaxies (SFGs) are expected to harbour an abundant reservoir of cosmic rays (CRs). At GeV energies, these CRs can undergo hadronic interactions with interstellar gases to produce 𝛾-rays, and the unresolved 𝛾-ray emission from populations of SFGs form a component of the extragalactic 𝛾-ray background (EGB). In this work, we investigate the contribution to the 0.01 -50 GeV EGB from SFG populations located up to redshift 𝑧 = 3. We consider their redshift evolution and variations in their physical properties, and model how this affects their contribution to the EGB. We find this is dominated by starbursts, while the contribution from main sequence SFGs is marginal at all energies. We also demonstrate that most of the 𝛾-ray contribution from SFGs emanates from low mass galaxies, with over 80 per cent of the emission originating from galaxies with stellar masses below 10 8 M . We show that the EGB at different energies captures different stages of the evolution of the source galaxies. At 0.01 GeV, the emission is dominated by galaxies at the noon of cosmic star-formation, around 𝑧 ∼ 2, however higher energy 𝛾-rays are instead mainly contributed from low mass starburst populations at higher redshifts, ∼ 700 Myr earlier. The redshift distributions of the EGB sources at different energies imprint intensity signatures at different angular scales, allowing their contribution to be distinguished using analyses of small-scale EGB intensity anisotropies. We show that the EGB is sensitive to the evolution of low mass populations of galaxies, particularly around 𝑧 ∼ 2 − 2.5, and that it provides a new means to probe the engagement of CRs in these galaxies before and during the high noon of cosmic star-formation.