The alkali–silica reaction (ASR) is a primary cause for premature concrete degradation. An accelerated mortar bar test is often used to access the detrimental phenomena in concrete caused by the ASR of aggregates. However, this test requires a certain environmental conditioning as per ASTM C1260. The objective of this study is to explore the effects of the cement alkali content, exposure solution concentration, temperature, and test duration on mortar bar expansion. Factorial experimental design and analysis was conducted to delineate the effects of the individual factors as well as their interaction. Five different aggregates with various mineralogical properties were used, representing reactive and non-reactive aggregates. Various dosages of cement alkalis (0.40, 0.80, and 1.20 Na2Oe), sodium hydroxide (NaOH) solution concentrations (0.5, 1.0, and 1.5 N), and temperature (40 °C, 80 °C, and 100 °C) were the studied variables. Mortar bar expansion was measured at 3, 7, 14, 21, 28, 56, and 90 days. Mortar bars incorporating Jhelum aggregates incurred expansion of 0.32% at 28 days, proving to be reactive aggregates as per ASTM C1260. Similarly, specimens incorporating Taxila aggregates showed expansion of 0.10% at 28 days, indicating non-reactive nature. It was observed that specimens with Sargodha aggregates showed expansion of 0.27% at 28 days for 0.50 N NaOH solution concentration compared to 0.31% expansion for identical specimens exposed to 1.5 N solution. Moreover, expansion increased with exposure duration for all the tested specimens. Experimental results showed that the cement alkali contents had relatively lesser effect on expansion for 1.0 N NaOH; while, in the case of 0.5 N and 1.5 N NaOH, the cement alkali had a significant effect. It was noted that expansion increased with an increase in the temperature. Jhelum aggregates showed 28-day expansion of 0.290% when exposed to 40 °C, but at a temperature of 100 °C, expansion increased to 0.339%. Factorial analysis revealed that the exposure solution had a major contribution towards the expansion of mortar bar specimens. This study highlights the contribution of various exposure conditions on the ASR expansion, which leads to a decisive role in selecting the aggregate sources for various applications and exposure conditions leading to sustainable construction.