Reducing cooling energy demand while achieving effective natural ventilation remains a key challenge in the design of buildings for hot-arid climates. Solar chimneys represent a viable passive strategy; however, their effectiveness is governed by complex interactions between geometric and operational parameters. To investigate this potential, scaled-down experimental model was constructed and tested under controlled conditions, and its results were used to validate the simulation model. Subsequently, a comprehensive parametric analysis involving 19,008 design alternatives was conducted, employing multi-objective optimization to explore trade-offs between airflow enhancement and cooling energy reduction. Sensitivity and correlation analyses identified chimney height, width (North–South), and window operability as the most influential factors, with regression models confirming strong predictive relationships with both objectives. Regression analysis showed high predictive accuracy for cooling energy (R² = 90.87%, test R² = 90.45%). The optimal designs featured chimney heights of 10.5–13.0 m, widths of 3.1–4.5 m (North–South axis), lengths of 1.1–2.2 m (East–West axis), window-to-wall ratio values between 0.45 and 0.80, and operable openings exceeding 76% on South and West facades. These configurations increased airflow rates from 1.15 m³/s to 2.67 m³/s and achieved cooling energy savings of 30–32% compared to the base case.