CO2 injection during geological CO2 storage (GCS) can result in large pressure build-ups that can limit the injection and reactivate existing faults. The extraction of resident brine from storage formations can alleviate such pressure rises. One critical challenge in applying an extraction well is determining the optimal well locations with reservoir simulation that could be an accurate approach but computationally inefficient. This work proposes the application of an Artificial Neural Network (ANN)-based proxy model in well-placement optimization problems involving pressure management of GCS. The effectiveness of the proposed approach was assessed by optimizing the placement of the CO2 injection and brine extraction wells in the upper aquifer of the Pohang Basin. Several ANN models with different input features were developed for the optimization study, and the best-performing model on the test data was selected. ANN integrated with a genetic algorithm was used to determine the optimal CO2 injection and brine production well locations that maximize the cumulative CO2 injected. Optimization was demonstrated using a full physics reservoir simulator to verify the results. Six hundred and twenty-two simulation runs were needed to reach the optimal solution using the simulator. Instead, with the proposed workflow, comparable results were achieved with only 120 simulation runs, reducing the number of simulation runs by 80.7%. Employing the ANN-based proxy model in the optimization study proved effective with good accuracy by providing a fast approximation to the full physics reservoir model.