This research presents an innovative stacked autoencoder-based receiver design to address the challenges of efficient signal recovery for low probability of detection (LPD) constrained covert underwater acoustic communication (CUAC), thereby promoting secure and eco-friendly communications in underwater environments. Communicating through underwater channels presents significant challenges due to the long propagation of acoustic waves, signal attenuation, and ambient noise. These challenges are further intensified in LPD-constrained CUAC systems due to severely degraded SNR of the received signal at the desired range. The proposed system employs a data-driven approach for receiver design to effectively recover the signal in a low SNR environment by learning intrinsic channel features and replaces traditional physical-layer operations of de-spreading, demodulation, and decoding with a unified, joint feature learning framework, creating an efficient processing pipeline and enhancing the BER performance of the receiver. The performance of the stacked autoencoder-based receiver is validated through a lake experiment conducted at a range of 1.22 km, along with simulations. The experiment demonstrates that the proposed receiver achieves reliable performance with SNR levels as low as -15 dB, yielding a significant 3 dB improvement at a BER of 10-2compared to conventional receivers.