Preliminary trajectory design is a global search problem that seeks multiple qualitatively different solutions to a trajectory optimization problem. Due to its high dimensionality and non-convexity, and the frequent adjustment of problem parameters, the global search becomes computationally demanding. In this paper, we exploit the clustering structure in the solutions and propose an amortized global search (AmorGS) framework. We use deep generative models to predict trajectory solutions that share similar structures with previously solved problems, which accelerates the global search for unseen parameter values. Our method is evaluated using De Jong's 5th function and a low-thrust circular restricted three-body problem.