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In this paper, neural networks are trained to learn the optimal time, the initial costates, and the optimal control law of time-optimal low-thrust interplanetary trajectories. The aim is to overcome the difficult selection of first guess costates in indirect optimization, which limits their implementation in global optimization and prevents on-board applications. After generating a dataset, three networks that predict the optimal time, the initial costate, and the optimal control law are trained. A performance assessment shows that neural networks are able to predict the optimal time and initial costate accurately, especially a 100% success rate is achieved when neural networks are used to initialize the shooting function of indirtect methods. Moreover, learning the state-control pairs shows that neural networks can be utilized in real-time, on-board optimal control.