We present a novel test generation algorithm for hardware accelerators of Spiking Neural Networks (SNNs). The algorithm is based on advanced optimization tailored for the spiking domain. It adaptively crafts input samples towards high coverage of hardware-level faults. Time-consuming fault simulation during test generation is circumvented by defining loss functions targeting the maximization of fault sensitisation and fault effect propagation to the output. Comparing the proposed algorithm to the existing ones on three benchmarks, it scales up for large SNN models, and it drastically reduces the test generation runtime from days to hours and the test duration from minutes to seconds. The resultant test input shows near perfect fault coverage and has a duration equivalent to a few dataset samples, thus, besides post-manufacturing testing, it is also suited for in-field testing.