We present a machine learning (ML) component designed to enhance the well-known branch-and-cut (B&C) framework for the symmetric traveling salesman problem (TSP) in which only the subtour elimination constraints (SECs) violated by previously found integer solutions are considered. The objective of the ML component is to identify which SECs, from a pool of candidates, will be required during the B&C execution and to add these constraints before initializing the framework. To develop this component, we investigate several intermediate questions, including evaluating various B&C implementations to identify the most effective one, determining the theoretical minimum and maximum number of SECs required by a given B&C implementation, generating a pool of SEC candidates, creating labeled data, engineering SEC-specific input features, and training the ML agent. We demonstrate that our trained agent slightly increases the number of instances solvable by our best B&C implementation and reduces the average computation time for these instances by 23%. We also show that these improvements extend to TSP instances with features different from those used to train the agent, although not consistently. While these improvements are already noteworthy, we also provide a proof of concept showing that reductions of up to 65% could be achieved with a “perfect” component, highlighting the potential of ML-integrated agents within exact optimization approaches. Although we acknowledge that, even when ML-augmented, the resulting B&C implementation still performs below the state-of-the-art Concorde algorithm, the proposed methodology is generalizable to other routing problems with SECs.