To aid urban air mobility (UAM), electric vertical takeoff and landing (eVTOL) aircraft are being targeted. Conventional multidisciplinary analysis and optimization (MDAO) can be expensive, while surrogate-based optimization can struggle with challenging physical constraints. This work proposes physics-constrained generative adversarial networks (physicsGAN), to intelligently parameterize the takeoff control profiles of an eVTOL aircraft and to transform the original design space to a feasible space. Specifically, the transformed feasible space refers to a space where all designs directly satisfy all design constraints. The physicsGAN-enabled surrogate-based takeoff trajectory design framework was demonstrated on the Airbus A3 Vahana. The physicsGAN generated only feasible control profiles of power and wing angle in the feasible space with around 98.9% of designs satisfying all constraints. The proposed design framework obtained 99.6% accuracy compared with simulation-based optimal design and took only 2.2 seconds, which reduced the computational time by around 200 times. Meanwhile, data-driven GAN-enabled surrogate-based optimization took 21.9 seconds using a derivative-free optimizer, which was around an order of magnitude slower than the proposed framework. Moreover, the data-driven GAN-based optimization using gradient-based optimizers could not consistently find the optimal design during random trials and got stuck in an infeasible region, which is problematic in real practice. Therefore, the proposed physicsGAN-based design framework outperformed data-driven GAN-based design to the extent of efficiency (2.2 seconds), optimality (99.6% accurate), and feasibility (100% feasible). According to the literature review, this is the first physics-constrained generative artificial intelligence enabled by surrogate models.