Aerodynamic shape optimization (ASO) plays a crucial role in aerodynamic design by enhancing an object’s aerodynamic performance while satisfying design constraints. Traditional ASO is costly and time-intensive, requiring extensive manual tuning to configure parameterization methods that define the design space and manipulate the shape geometry. These conventional parameterization methods limit flexibility and require extensive domain prior knowledge on the design tasks and geometric processing, making efficient and accessible ASO a challenge. We present the Deep Geometric Mapping (DeepGeo) model, a neural network-based method to fully automate the parametrization that accelerates ASO and reduces the cost. By leveraging the universal approximation capabilities of neural networks, DeepGeo achieves large shape deformation freedom while maintaining global smoothness, facilitating efficient optimization in the high-dimensional design space. By integrating the Computational Fluid Dynamics (CFD) mesh deformation within its framework, DeepGeo simplifies the ASO pipeline. By eliminating the need for any training dataset and manual hyperparameter tuning, DeepGeo further significantly reduces implementation complexity and cost. We validate our approach through diverse case studies--including two-dimensional circle optimization, three-dimensional Common Research Model (CRM) wing optimization, and Blended-Wing-Body aircraft design--all using identical settings. Results demonstrate performance comparable to state-of-the-art free-form deformation method while requiring minimal human intervention. This work establishes DeepGeo as a transformative tool for automating ASO and democratizing advanced design optimization techniques.