Flexible pavements are mostly affected by meteorological factors in addition to traffic loads, which results in premature pavement failures like rutting and moisture-induced damage. This study focuses on the impacts of adding various contents of nano-silica (NS), i.e., 2%, 4%, 6%, and 8% (percentage weight of asphalt), along with a constant value of 4.5% styrene-butadiene-styrene (SBS). To assess the effectiveness of modified and unmodified mixtures, the indirect tensile strength (ITS) test, resilient modulus (MR) test, and wheel tracking test were conducted. The MR test was performed at dual temperature values, i.e., 25 °C and 40 °C, and demonstrated different metrological conditions in this region. The tensile strength ratio was used to estimate the mitigation of water losses in hot mix asphalt (HMA) mixtures (specimens) utilizing ITS test results of the conditioned and unconditioned specimens. Moreover, a model was developed for the rutting potential of the modified specimens using multi expression programming (MEP), a sophisticated technique that employs experimental data and suggests an equation for different input variables. The results indicated that the addition of NS to SBS-modified bitumen enhanced different mechanical properties of the specimens, including the stiffness and moisture and rutting resistances. The temperature had adverse effects on the stiffness of the specimens, while the modifiers had a direct relationship with the stiffness. The two-way factorial method justified the effect of the temperature and modifiers on MR with 95% precision, while the MEP model for rutting showed an R² value of >0.95, which revealed a good relationship between the experimental and predicted data. Furthermore, NS and SBS had a good impact on the mechanical properties of the HMA specimens.