The accurate estimation of cradle-to-gate embodied carbon at the early design stage remains a critical challenge for structural and construction engineers, particularly where detailed Life Cycle Assessment data are unavailable during permitting. This study presents a data-driven framework to predict and attribute the Modules A1–A3 carbon footprint of mid-rise reinforced concrete frame structures using only bill-of-quantities (BOQ) data. Based on 812 residential construction permits from Tehran Municipality (2015–2024), an extreme gradient boosting model was trained within a nested cross-validation scheme and interpreted via out-of-sample Shapley additive explanations to quantify the predictive influence of seven material quantity classes. The results reveal that while reinforcement steel and concrete remain primary drivers, secondary materials—particularly cellular lightweight concrete and gypsum plaster—achieve disproportionately high explanatory importance by acting as statistical proxies for carbon-intensive construction archetypes and finishing regimes. However, severe multicollinearity inherent in BOQ data (VIF > 100 for four materials) causes secondary features to degrade predictive stability when combined with primary structural variables. Furthermore, material importance rankings exhibit poor cross-fold stability (mean Kendall's τ = 0.238), indicating that hierarchies derived from a single data split may not be robust. The framework offers engineers a transparent, rigorously validated tool for early-stage carbon screening and targeted material-based decarbonisation using readily available permitting data.