Mapping soil organic carbon (SOC) stock can serve as a resilience indicator for climate change. As part of the carbon dioxide (CO2) sink, soil has recently become an integral part of the global carbon agenda to mitigate climate change. We used hyperspectral remote sensing to model the SOC stock in the Sele River plain located in the Campania region in southern Italy. To this end, a soil spectral library (SSL) for the Campania region was combined with an aerial hyperspectral image acquired with the AVIRIS–NG sensor mounted on a Twin Otter aircraft at an altitude of 1433 m. The products of this study were four raster layers with a high spatial resolution (1 m), representing the SOC stocks and three other related soil attributes: SOC content, clay content, and bulk density (BD). We found that the clay minerals’ spectral absorption at 2200 nm has a significant impact on predicting the examined soil attributes. The predictions were performed by using AVIRIS–NG sensor data over a selected plot and generating a quantitative map which was validated with in situ observations showing high accuracies in the ground-truth stage (OC stocks [RPIQ = 2.19, R2 = 0.72, RMSE = 0.07]; OC content [RPIQ = 2.27, R2 = 0.80, RMSE = 1.78]; clay content [RPIQ = 1.6 R2 = 0.89, RMSE = 25.42]; bulk density [RPIQ = 1.97, R2 = 0.84, RMSE = 0.08]). The results demonstrated the potential of combining SSLs with remote sensing data of high spectral/spatial resolution to estimate soil attributes, including SOC stocks.