In this paper, we present a deep learning architecture for the operation of designing optimized physical geometries for which prescribed performance metrics in steady-state fluid flow scenarios hold. We use a U-Net-based neural network architecture as a learned surrogate model and implement an efficient gradient-based inversion method. Leveraging the inherent differentiability of the trained model, our approach regenerates geometries with desired aerodynamic properties. Numerical results for the 2D synthetic cases show significant drag reduction and lift increment with respect to reference shapes. This work lays the groundwork for automatic design exploration involving neural network surrogates that are a computationally efficient alternative to conventional CFD-based optimization loops.