Forecasting volatility in the USD/IDR exchange rate poses a critical challenge for Indonesia's financial stability, especially given how the data tends to display non-linear characteristics along with extreme outliers—what we commonly call fat-tails. This research develops a hybrid EGARCH-LSTM architecture to address these challenges by bringing together the precision of econometric modeling with deep learning's adaptability. Our dataset consists of 2,605 daily observations of the USD to IDR exchange rate ranging from 2015 to 2025. We extract volatility features using an EGARCH(1, 1) model with a t-distribution, which will then be entered as exogenous input into a Long-Short-Term Memory (LSTM) network. Our analysis shows a strong contrast between price predictions and risk estimates. In terms of price forecasting, the market demonstrates remarkable efficiency. The simple Naive Forecast, with an RMSE of 100.47, proved extremely difficult to outperform, lending support to the Random Walk Hypothesis. However, the Hybrid EGARCH-LSTM demonstrated superior volatility prediction capabilities, achieving the lowest Out-of-Sample Volatility MAE of 0.0075 compared to 0.0083 for the standalone EGARCH model. The EGARCH-LSTM hybrid model achieved the best performance, passed the Kupiec backtest (P-value = 0.4373), and significantly outperformed the pure econometric model, which failed due to excessive conservatism in its estimation. This study concludes that although accurate price predictions are still unattainable in efficient markets, the EGARCH-LSTM hybrid architecture provides a powerful and reliable tool for risk estimation. These results offer significant implications for hedging and risk management practices in the Indonesian foreign exchange market.