This study investigates the influence of geometric parameters—size, proportions, number of floors, and roof shape—on the environmental efficiency of family houses using a simplified life cycle assessment (LCA) method. The analysis focuses on the product stage (A1–A3), commonly referred to as “cradle to gate,” which encompasses embodied emissions and energy. It demonstrates that even within the limited scope of the product stage (A1–A3), geometric parameters such as floor area, proportions, and compactness exert a decisive influence on embodied environmental impacts. In addition to absolute and per-square-meter indicators, the analysis highlights the importance of the shape factor, defined as the ratio of envelope area to heated volume, as a fairer basis for comparing buildings of different geometries. Similar to its established role in operational energy certification, the shape factor provides a meaningful link between geometry and embodied impacts. The findings suggest that future implementation of the Energy Performance of Building Directive IV (EPBD IV, EU 2024/1275), which mandates the calculation of the global warming potential (GWP) of new buildings from 2028 onwards, could benefit from evaluating both primary energy non-renewable (PENRT) and global warming potential (GWP) in relation to the shape factor, once sufficient data become available. The presented study thus contributes to the ongoing European debate on whole-life-cycle carbon assessment while clarifying its novelty as a geometry-based, product-stage method that can be scaled and adapted to different contexts. The proposed simplified, geometry-oriented approach to estimating embodied impacts (A1–A3) with shape factor-based normalisation enables a fair comparison of buildings with different geometries at the concept stage.