Synthetic biology leverages engineering principles to program biology with new functions for applications in medicine, energy, food, and the environment. A central aspect of synthetic biology is the creation of synthetic gene circuits - engineered biological circuits capable of performing operations, detecting signals, and regulating cellular functions. Their development involves large design spaces with intricate interactions among circuit components and the host cellular machinery. Here, we discuss the emerging role of machine learning in addressing these challenges. We articulate how machine learning may enhance synthetic gene circuit engineering, from individual components to circuit-level aspects, while highlighting associated challenges. We discuss potential hybrid approaches that combine machine learning with mechanistic modeling to leverage the advantages of data-driven models with the prescriptive ability of mechanism-based models. Machine learning and its integration with mechanistic modeling are poised to advance synthetic biology, but challenges need to be overcome for such efforts to realize their potential.