Real-time robotic systems require advanced perception, computation, and action capability. However, the main bottleneck in current autonomous systems is the trade-off between computational capability, energy efficiency and model determinism. World modeling, a key objective of many robotic systems, commonly uses occupancy grid mapping (OGM) as the first step towards building an end-to-end robotic system with perception, planning, autonomous maneuvering, and decision making capabilities. OGM divides the environment into discrete cells and assigns probability values to attributes such as occupancy and traversability. Existing methods fall into two categories: traditional methods and neural methods. Traditional methods rely on dense statistical calculations, while neural methods employ deep learning for probabilistic information processing. In this study, we propose a vector symbolic architecture-based OGM system (VSA-OGM) that retains the interpretability and stability of traditional methods with the improved computational efficiency of neural methods. Our approach, validated across multiple datasets, achieves similar accuracy to covariant traditional methods while reducing latency by approximately 45x and memory by 400x. Compared to invariant traditional methods, we see similar accuracy values while reducing latency by 5.5x. Moreover, we achieve up to 6x latency reductions compared to neural methods while eliminating the need for domain-specific model training. This work demonstrates the potential of vector symbolic architectures as a practical foundation for real-time probabilistic mapping in autonomous systems operating under strict computational and latency constraints.