The CPU-based system is widely used for simulating the brain-inspired spiking neural networks (SNN) by taking the benefit of flexibility, while processing high input spiking rates caused by immature coding mechanism costs many CPU cycles, and the introduction of additional information required by serial execution needs the time-consuming pre- and post-neuron matching algorithm. To address these issues, we propose an algorithm set leveraging the multiply-accumulate (MAC) array to accelerate the SNN inference. By rearranging and compressing operands losslessly, we retain the advantage of the MAC array on fast parallel computing, as well as alleviate the ineffective memory occupation and the waste of computing resources, which result from the inherent sparse feature of SNN and reluctant memory alignment from fixed MAC hardware structure. Benchmarking with an SNN radar gesture recognition model, the algorithms jointly optimize 82.71% of the execution time compared to the serial computation on the ARM M4F of the SpiNNaker 2 chip; 49.89% of the memory footprint is reduced contrasted with the unoptimized MAC calculation. This article explicitly expands the application field of the General Sparse Matrix-Matrix Multiplication (SpGEMM) issue to SNN, developing novel SpGEMM optimization algorithms fitting the SNN feature and MAC array.