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Spiking Neural Networks (SNNs) have been considered a potential competitor to Artificial Neural Networks (ANNs) due to their high biological plausibility and energy efficiency. However, the architecture design of SNN has not been well studied. Previous studies either use ANN architectures or directly search for SNN architectures under a highly constrained search space. In this paper, we aim to introduce much more complex connection topologies to SNNs to further exploit the potential of SNN architectures. To this end, we propose the topology-aware search space, which is the first search space that enables a more diverse and flexible design for both the spatial and temporal topology of the SNN architecture. Then, to efficiently obtain architecture from our search space, we propose the spatio-temporal topology sampling (STTS) algorithm. By leveraging the benefits of random sampling, STTS can yield powerful architecture without the need for an exhaustive search process, making it significantly more efficient than alternative search strategies. Extensive experiments on CIFAR-10, CIFAR-100, and ImageNet demonstrate the effectiveness of our method. Notably, we obtain 70.79% top-1 accuracy on ImageNet with only 4 time steps, 1.79% higher than the second best model. Our code is available under https://github.com/stiger1000/Random-Sampling-SNN. • The SNN architectures significantly benefit from much more complex connection topologies. • Incorporating synaptic delay provides a novel perspective to the design of SNN architectures. • The novel sampling method greatly accelerates the process of obtaining SNN architectures. [ABSTRACT FROM AUTHOR]