The energy retrieval process in an Enhanced Geothermal System (EGS) depends on fracture networks to facilitate fluid movement, thereby enabling the extraction of heat from adjacent rocks matrix. Nonetheless, due to the inherent heterogeneity and intricate multi-physics characteristics of these systems, high-fidelity physics-based forward simulations ($f_h$) can be computationally demanding. This presents a considerable obstacle to the efficient management of these reservoirs. Therefore, creating an effective and robust optimization framework is essential, with the primary aim being to maximize the thermal extraction from Enhanced Geothermal Systems (EGS). A deep learning-assisted reservoir management framework incorporating a low-fidelity forward surrogate model ($f_l$) alongside gradient-based optimizers is developed to expedite reservoir management. A thermo-hydro-mechanical (THM) model for EGS is established by utilizing finite element-based reservoir simulation techniques. By parameterizing the fracture aperture and well controls, we carried out the THM simulation to produce 2500 datasets. Subsequently, we employed these datasets to train two distinct deep neural network (DNN) architectures to predict the variations in pressure and temperature distributions. Ultimately, these predictions from the forward model are used in calculating the total net energy. Instead of executing the optimization workflow with a large number of simulations from $f_h$, we directly optimize the well control parameters relative to the geological parameters using $f_l$. Since $f_l$ is efficient and fully differentiable, it could be combined with various gradient-based or gradient-free optimization algorithms to maximize the total net energy by determining the optimal decision parameters. Drawing from the simulation datasets, we analysed the effect of fracture aperture variation on temperature and pressure evolution. Our investigation revealed that the spatial distribution of the fracture aperture is a predominant factor in controlling the propagation of the thermal front. Variations of the fracture aperture exhibit a strong correlation with temperature fluctuations within the fracture, primarily due to thermal stress changes. When compared with a comprehensive physics simulator, our DNN-based forward surrogate model offers a significant computational acceleration, approximately 1500 times faster, without compromising predictive accuracy, achieving an $R^2$ value of 99%. The forward model $f_l$, when combined with gradient-based optimizers, enables optimization to proceed 10 to 68 times faster than when using derivative-free global optimizers. The proposed reservoir management framework exhibits both efficiency and scalability, facilitating the real-time execution of each optimization process.