This study addresses the need for advanced machine learning-based process monitoring in smart manufacturing. A methodology is developed for near-real-time part quality prediction based on process-related data obtained from a CNC turning center. Instead of the manual feature extraction methods typically employed in signal processing, a novel one-dimensional convolutional architecture allows the trained model to autonomously extract pertinent features directly from the raw signals. Several signal channels are utilized, including vibrations, motor speeds, and motor torques. Three quality indicators—average roughness, peak-to-valley roughness, and diameter deviation—are monitored using a single model, resulting in a compact and efficient classifier. Training data are obtained via a small number of experiments designed to induce variability in the quality metrics by varying feed, cutting speed, and depth of cut. A sliding window technique augments the dataset and allows the model to seamlessly operate over the entire process. This is further facilitated by the model’s ability to distinguish between cutting and non-cutting phases. The base model is evaluated via k-fold cross validation and achieves average F1 scores above 0.97 for all outputs. Consistent performance is exhibited by additional instances trained under various combinations of design parameters, validating the robustness of the proposed methodology.