One-part geopolymer concrete/mortar is a pre-mixed material made from industrial by-products and solid alkaline activators that only requires the addition of water for activation. Apart from being environmentally friendly, it also reduces complexity and improves consistency in the mixing process, leading to more efficient production and consistent material properties. However, developing one-part geopolymer concrete with desirable compressive strength is challenging because of the complexity of the chemical reaction involved, the variability of the raw materials used, and the need for precise control of curing conditions. Therefore, 80 different one-part geopolymer mixtures were compiled from the open literature in this study, and the effects of the constituent materials, the dosage of alkaline activators, curing condition, and water/binder ratio on the 28-day compressive strength of one-part geopolymer paste were examined in detail. An ANN model with the Levenberg–Marquardt algorithm was developed to estimate one-part geopolymer’s compressive strength and its sensitivity to binder constituents and alkaline dosage. The ANN model’s weights and biases were also used to develop a CPLEX-based optimization method for achieving maximum compressive strength. The results confirm that the compressive strength of one-part geopolymer pastes increased by increasing the Na2O content of the alkaline source and the slag dosage; however, increasing the Na2O content in alkaline sources beyond 6% by fly ash weight led to decreasing the compressive strength; therefore, the optimum alkaline activator dosage by weight of fly ash was to be 12% (i.e., 6% Na2O). The proposed ANN model developed in this study can aid in the production and performance tuning of sustainable one-part geopolymer concrete and mortar for broader full-scale applications.