Accurate prediction of building carbon emissions during early design remains a critical yet Accurate carbon footprint estimation during the design and permitting stages is critical for effective embodied carbon mitigation, yet conventional Life Cycle Assessment methods require detailed data that are rarely available before construction. This study presents a cross-stage estimation framework that exploits latent relationships between construction lifecycle phases to enable reliable carbon forecasting from sparse early-stage inputs. Based on 1,158 real-world building projects, the framework transfers information from data-rich manufacturing-stage inventories to data-scarce permitting and construction stages. Two scenarios were evaluated: predicting manufacturing-phase carbon from minimal permitting parameters, and forecasting construction-phase emissions using manufacturing-stage data. The proposed approach substantially outperformed conventional single-stage methods, achieving R² improvements of 39.6% and 36.8%, respectively. These findings confirm that systematic exploitation of cross-stage relationships can deliver accurate pre-construction carbon estimates without requiring complete material inventories at the design stage. The framework provides construction engineers and regulatory bodies with a practical tool for early carbon screening, enabling a shift from post-construction compliance to proactive design-phase mitigation strategies. The proposed approach enables data-efficient, scalable, and lifecycle-aligned carbon estimation, offering actionable value to municipal permitting authorities, urban planners, and design professionals seeking to integrate carbon intelligence into early decision-making.