With the progressive reduction in virgin material availability and the growing global concern for sustainability, civil engineering researchers worldwide are shifting their attention toward exploring alternative and mechanically sound technological solutions. The feasibility of preparing both cold and hot asphalt mixtures (AMs) for road pavement binder layers with construction and demolition wastes (C&DWs) and reclaimed asphalt pavement (RAP) partially replacing virgin materials like limestone aggregates and filler has already been proven. The technical suitability and compliance with technical specifications for road paving materials involved the evaluation of mechanical and volumetric aspects by means of indirect tensile strength tests and saturated surface dry voids, respectively. Thus, the main goal of the present study is to train, validate, and test selected machine learning algorithms based on data obtained from the previous experimental campaign with the aim of predicting the volumetric properties and the mechanical performance of the investigated mixtures. A comparison between the predictions made by ridge and lasso regression techniques and both shallow (SNN) and deep neural network (DNN) models showed that the latter achieved better predictive capabilities, highlighted by fully satisfactory performance metrics. DNN performance can be summarized by R2 values equal to 0.8990 in terms of saturated surface dry void predictions, as well as 0.9954 in terms of indirect tensile strength predictions. Predicted observations can be thus implemented within the traditional mix design software. This would reduce the need to carry out additional expensive and time-consuming experimental campaigns.