In the design process, structural engineers tend to play a restricted role in the sustainable performance of buildings, as the decisions are usually in the hands of architects and clients. Evidently, the types of structures have significant effects on the land use, energy demand, and carbon emissions of buildings. This paper presents an extensive review of currently adopted sustainable structural design strategies, thereby emphasizing the need for a comprehensive optimization approach to minimize the buildings’ carbon footprint. However, a design optimization problem involves hundreds of design variables and requires long computation time. To overcome these issues, a parametric study should be prior conducted to estimate the interrelationships and the influence of structural design variables on the final embodied emissions. In this research, a flat plate building is investigated considering different column spacings, concrete strengths, structural component sizes, detailed reinforcements, and for the application of Reinforced Concrete (RC) and Post-Tensioned (PT) construction techniques. While the most sustainable designs of slab systems are attained with shorter slab spans and thinner slab depths, columns having less longitudinal reinforcement with a moderate rise in dimensions are the best options. Furthermore, the employment of pre-stressed tendons results in a significant decrease in material requirements and related embodied impacts, by 26.3–33.5% and 26.6–33.8%, respectively. The outcomes indicated that reduction in a building's self-weight does not necessarily mean a decline in embodied emissions, highlighting the trade-offs between material saving and material carbon intensiveness in the decisions towards sustainable design and construction.