The advancement of future large-scale wireless networks necessitates the development of cost-effective and scalable security solutions. Conventional cryptographic methods, due to their computational and key management complexity, are unable to fulfill the low-latency and scalability requirements of these networks. Physical layer (PHY) security has been put forth as a cost-effective alternative to cryptographic mechanisms that can circumvent the need for explicit key exchange between communication devices, owing to the fact that PHY security relies on the physics of the signal transmission for providing security. In this work, a space-time-modulated digitally-coded metamaterial (MTM) leaky wave antenna (LWA) is proposed that can enable PHY security by achieving the functionalities of directional modulation (DM) using a machine learning-aided branch and bound (B&B) optimized coding sequence. From the theoretical perspective, it is first shown that the proposed space-time MTM antenna architecture can achieve DM through both the spatial and spectral manipulation of the orthogonal frequency division multiplexing (OFDM) signal received by a user equipment. Simulation results are then provided as proof-of-principle, demonstrating the applicability of our approach for achieving DM in various communication settings. To further validate our simulation results, a prototype of the proposed architecture controlled by a field-programmable gate array (FPGA) is realized, which achieves DM via an optimized coding sequence carried out by the learning-aided branch-and-bound algorithm corresponding to the states of the MTM LWA's unit cells. Experimental results confirm the theory behind the space-time-modulated MTM LWA in achieving DM, which is observed via both the spectral harmonic patterns and bit error rate (BER) measurements.