The cement industry is a significant contributor to CO₂ emissions worldwide, which demands new measures to reduce its environmental impacts. Therefore, finding solutions to reduce the CO₂ emissions in cement production became necessary. Pozzolanic materials offer an optimum solution approach with both environmental and functional advantages. For the investigation of pozzolan effects on the concrete mixture, the modeling part becomes a challenging task. This study models and predicts the compressive strength of pozzolanic cement-based concrete using deep residual neural networks (DRNNs) and variance-based sensitivity analysis (VBSA). The designed DRNNs architecture uses shortcuts (i.e., residual connections) that bypass some layers in the deep network structure in order to alleviate the problem of training with high accuracy. The research also examines crucial aspects such as pozzolan type, substitution ratio, component proportions, and grinding processes, using data developed by the authors and from different pozzolanic concrete compositions from various studies. The proposed model showed a high accuracy of R² = 0.94 for testing data that outperformed traditional literature models, enabling the generation of a large sample of synthetic experimental data for further analysis. The VBSA improves knowledge by prioritizing the importance of input factors, resulting in a complete method for designing concrete mixes. The analysis revealed that silica fume and volcanic ash were the most effective pozzolans in enhancing compressive strength, followed by scoria and metakaolin, with optimal substitution ratios ranging from 10 to 15% for most natural pozzolans and up to 20–30% for metakaolin and pumicite. Hence, this newly presented analysis framework offers an optimizing tool for pozzolanic concrete mix design that could investigate several pozzolana types/proportions, their efficiency, and the structural performance of the final concrete mixture.