Spacecraft rendezvous enables on-orbit servicing, debris removal, and crewed docking, forming the foundation for a scalable space economy. Designing such missions requires rapid exploration of the tradespace between control cost and flight time across multiple candidate targets. However, multi-objective optimization in this setting is challenging, as the underlying constraints are often nonconvex, and mission designers must balance accuracy (e.g., solving the full problem) with efficiency (e.g., convex relaxations), slowing iteration and limiting design agility. To address these challenges, this paper proposes an AI-powered framework that enables agile and generalized rendezvous mission design. Given the orbital information of the target spacecraft, boundary conditions of the servicer, and a range of flight times, a transformer model generates a set of near-Pareto optimal trajectories across varying flight times in a single parallelized inference step, thereby enabling rapid mission trade studies. The model is further extended to accommodate variable flight times and perturbed orbital dynamics, supporting realistic multi-objective trade-offs. Validation on chance-constrained rendezvous problems in Earth orbits with passive safety constraints demonstrates that the model generalizes across both flight times and dynamics, consistently providing high-quality initial guesses that converge to superior solutions in fewer iterations. Moreover, the framework efficiently approximates the Pareto front, achieving runtimes comparable to convex relaxation by exploiting parallelized inference. Together, these results position the proposed framework as a practical surrogate for nonconvex trajectory generation and mark an important step toward AI-driven trajectory design for accelerating preliminary mission planning in real-world rendezvous applications.