The present research article investigates the extraction of aluminum (Al) from an engineered CaO-Al2O3-SiO2 slag by leaching with aqueous HCl under atmospheric pressure conditions. The slag is the by-product of an aluminothermic reduction process to produce metallurgical-grade silicon (Si) in a more sustainable way compared to conventional carbothermic reduction. One major challenge in the acidic leaching of aluminosilicate materials, like the slag treated in this study, is the possibility of SiO2 gel formation during the leaching process. Extensive SiO2 gel formation can make the separation of pregnant leach solution (PLS) from the leached residue impossible. Consequently, any acid leaching of aluminosilicate materials must be optimized for avoidance of these gelation phenomena. The present study first explores the leaching behavior of the calcium aluminosilicate slag in relation to the S/L ratio, with all other hydrometallurgical factors remaining stable (20.2% wt. HCl solution, 80 °C, optimized stirring rate), to determine at which value of this parameter SiO2 gelation occurs. After determining the optimum S/L ratio for this system, an analysis of the behavior of Si in the PLS is presented, and the mechanism of SiO2 gelation is explained based on critical assessment of these results against data provided from the scientific literature. It was found that the value of the pH of the PLS and the concentration of dissolved CaCl2 and AlCl3 are critical factors for the formation of filterable amorphous SiO2. Under the optimum leaching conditions, PLS containing 37 g/L Al was obtained with concurrent avoidance of gelation phenomena.