Portland cement concrete (PCC) is the construction material most used worldwide. Hence, its proper characterization is fundamental for the daily-basis engineering practice. Nonetheless, the experimental measurements of the PCC’s engineering properties (i.e., Poisson’s Ratio -v-, Elastic Modulus -E-, Compressive Strength -ComS-, and Tensile Strength -TenS-) consume considerable amounts of time and financial resources. Therefore, the development of high-precision indirect methods is fundamental. Accordingly, this research proposes a computational model based on deep neural networks (DNNs) to simultaneously predict the v, E, ComS, and TenS. For this purpose, the Long-Term Pavement Performance database was employed as the data source. In this regard, the mix design parameters of the PCC are adopted as input variables. The performance of the DNN model was evaluated with 1:1 lines, goodness-of-fit parameters, Shapley additive explanations assessments, and running time analysis. The results demonstrated that the proposed DNN model exhibited an exactitude higher than 99.8%, with forecasting errors close to zero (0). Consequently, the machine learning-based computational model designed in this investigation is a helpful tool for estimating the PCC’s engineering properties when laboratory tests are not attainable. Thus, the main novelty of this study is creating a robust model to determine the v, E, ComS, and TenS by solely considering the mix design parameters. Likewise, the central contribution to the state-of-the-art achieved by the present research effort is the public launch of the developed computational tool through an open-access GitHub repository, which can be utilized by engineers, designers, agencies, and other stakeholders.