In the study, the effect of 4% sodium sulfate (Na2SO4) as an activator on cement pastes with 0%, 20%, and 40% fly-ash replacements and a low water-to-cementitious materials ratio of 0.30 was investigated. The investigation was conducted to evaluate the effectiveness of the technique for the utilization of fly ash in developing sustainable concrete. The use of Na2SO4 decreased setting times of the fresh pastes and increased compressive strength of the hardened pastes up to 28 days irrespective of fly-ash replacement. The use decreased Ca(OH)2 content in the hardened pastes irrespective of fly-ash replacement. Meanwhile, it increased Ca(OH)2 consumption by the pozzolanic reaction of fly ash and content of calcium silicate and aluminate hydrates in the hardened fly-ash–cement pastes. Consequently, the use of Na2SO4 negatively affected cement hydration in the hardened cement pastes without fly ash, while it accelerated ettringite formation and pozzolanic reaction of fly ash in the hardened pastes.