In recent years, the power demonstrated by Machine Learning (ML) has increasingly attracted the interest of the optimization community that is starting to leverage ML for enhancing and automating the design of algorithms. One combinatorial optimization problem recently tackled with ML is the Job Shop scheduling Problem (JSP). Most of the works on the JSP using ML focus on Deep Reinforcement Learning (DRL), and only a few of them leverage supervised learning techniques. The recurrent reasons for avoiding supervised learning seem to be the difficulty in casting the right learning task, i.e., what is meaningful to predict, and how to obtain labels. Therefore, we first propose a novel supervised learning task that aims at predicting the quality of machine permutations. Then, we design an original methodology to estimate this quality, and we use these estimations to create an accurate sequential deep learning model (binary accuracy above 95%). Finally, we empirically demonstrate the value of predicting the quality of machine permutations by enhancing the performance of a simple Tabu Search algorithm inspired by the works in the literature.