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Efficient job scheduling is a critical challenge in modern computing environments, particularly in cloud computing, high-performance computing (HPC), and real-time systems. Traditional software-based schedulers struggle to efficiently balance workload distribution due to high scheduling overhead, lack of adaptability to dynamic workloads, and suboptimal resource utilization. This research presents a novel FPGA-based accelerator for stochastic online scheduling (SOS), leveraging hardware parallelism to optimize real-time job allocation and reduce scheduling latency. By introducing a hardware-accelerated approach to real-time scheduling, this research establishes a new paradigm for adaptive scheduling mechanisms in computing systems. The FPGA-based SOS accelerator provides a scalable, energy-efficient, and high-performance alternative to software-based scheduling, making it particularly well suited for cloud data centers, AI workloads, and latency-sensitive applications. Future extensions include AI-driven scheduling optimization, multi-FPGA distributed scheduling architectures, and integration with carbon-aware computing frameworks to further enhance efficiency and sustainability.