Depression is a prevalent neuropsychiatric disorder whose clinical diagnosis often suffers from subjectivity and inconsistency. Electroencephalography (EEG), as an objective neurophysiological technique, provides a non-invasive, low-cost, and high–temporal-resolution approach for depression detection. However, the application of EEG in real-time and embedded diagnostic systems remains constrained by high data dimensionality, computational complexity, and limited model interpretability. To address these challenges, this study proposes a hybrid diagnostic framework integrating a Convolutional Neural Network (CNN) and a Long Short-Term Memory (LSTM) network, combined with a Genetic Algorithm (GA)–based multi-objective lead selection strategy. The CNN–LSTM model effectively extracts both spatial and temporal features from EEG signals, while the GA-based optimization identifies an optimal subset of EEG leads that balances diagnostic accuracy, computational efficiency, and physiological interpretability. Experimental results demonstrate that the proposed approach reduces the number of EEG channels from 62 to 19 (a 70% reduction) while improving the classification accuracy from 0.9027 to 0.9715 and the F1 score from 0.9057 to 0.9673. Meanwhile, total parameters and memory usage are reduced by 8.3% and 5.6%, respectively, enabling faster inference and lower hardware requirements. The selected electrodes are primarily distributed across the prefrontal, temporal, and parietal regions—areas known to be associated with depressive neural activity—thereby reinforcing the biological interpretability of the model. Overall, the proposed GA-optimized CNN–LSTM framework achieves an effective balance between accuracy, efficiency, and interpretability, offering a reliable foundation for developing lightweight, real-time, and clinically deployable EEG-based depression diagnostic systems.