Passive sky radiative cooling systems, which utilize the universe as a natural heat sink, offer promising low-carbon solutions for urban cooling. Surface downwelling longwave radiation (SDLR), originating from the atmosphere, significantly influences the cooling potential of such systems. However, spatiotemporal continuous SDLR data remain scarce, primarily due to the complex dynamics of clouds and their non-linear interactions with radiation. To address this challenge, we propose a novel two-stage surrogate modeling framework that combines high-resolution (5-min, 2-km) geostationary satellite imagery with deep learning techniques. When validated against one year (2019) of SDLR measurements from the Surface Radiation Budget Network (SURFRAD) across diverse climatic regions in the contiguous United States, the proposed model significantly outperforms direct end-to-end satellite-to-SDLR mapping, with MBE values ranging from 0.10 W/m2 to 17.62 W/m2 and RMSE ranging from 20.78 W/m2 to 30.54 W/m2. Benchmark comparisons underscore its reliability over empirical, physical, reanalysis, and satellite-based methods, which demonstrate competitive performance with notable bias reduction. Furthermore, this model enables robust and efficient retrieval of spatiotemporal cloud properties and SDLR, while exhibiting strong transferability and minimal reliance on ground-based data, thereby supporting real-time, regional-scale operational applications.