Inertial navigation systems (INS) are widely used in both manned and autonomous platforms. One of the most critical tasks prior to their operation is to accurately determine their initial alignment while stationary, as it forms the cornerstone for the entire INS operational trajectory. While low-performance accelerometers can easily determine roll and pitch angles (leveling), establishing the heading angle (gyrocompassing) with low-performance gyros proves to be a challenging task without additional sensors. This arises from the limited signal strength of Earth's rotation rate, often overridden by gyro noise itself. To circumvent this deficiency, in this study we present a practical deep learning framework to effectively compensate for the inherent errors in low-performance gyroscopes. The resulting capability enables gyrocompassing, thereby eliminating the need for subsequent prolonged filtering phase (fine alignment). Through the development of theory and experimental validation, we demonstrate that the improved initial conditions establish a new lower error bound, bringing affordable gyros one step closer to being utilized in high-end tactical tasks.