Modern component design relies on virtual environments to simulate and optimize performance characteristics. This optimization process can be computationally demanding due to the solution of complex optimization problems governed by Partial Differential Equations (PDEs). Gradient-based optimization methods are often employed due to their superior convergence properties, while the adjoint technique is employed to further reduce the computational cost of gradient evaluation. However, even adjoint-based optimization may not be sufficient to significantly reduce computational cost. To address this challenge, this paper introduces a novel one-shot acceleration technique based on a fully coupled Newton method. Unlike conventional adjoint-based optimization, which sequentially solves the PDEs and optimization problem, the proposed one-shot approach simultaneously couples the solution of these two processes. This approach involves applying the Newton method to the KKT optimality conditions, resulting in a quadratic convergence rate towards the optimal solution. The selected test case involves the inverse design of a 2D nozzle, with the objective of matching a specified pressure distribution within the nozzle. The full-3D, coupled, compressible solver of CADO is employed for a simplified, 2D, inviscid test case. The presented methodology is however readily applicable to other 3D test cases that share the same simplicity in the mesh generation. The findings of this research represent a first step towards the development of a new methodology for enhancing the computational performance of gradient-based, adjoint methods.