We propose an extension of symbolic execution of distributed systems to test software parts related to timing. Currently, the execution model is limited to symbolic input for individual nodes, not capturing the important class of timing errors resulting from varying network conditions. In this paper, we introduce symbolic system time in order to systematically find timing-related bugs in distributed systems. Instead of executing time events at a concrete time, we execute them at a set of times and analyse possible event interleaving son demand. We detail on the resulting problem space, discuss possible algorithmic optimisations, and highlight our future research directions.