While existing studies have highlighted the advantages of deep learning (DL)-based joint source-channel coding (JSCC) schemes in enhancing transmission efficiency, they often overlook the crucial aspect of resource management during the deployment phase. In this paper, we propose an approach to minimize the transmission latency in an uplink JSCC-based system. We first analyze the correlation between end-to-end latency and task performance, based on which the end-to-end delay model for each device is established. Then, we formulate a non-convex optimization problem aiming at minimizing the maximum end-to-end latency across all devices, which is proved to be NP-hard. We then transform the original problem into a more tractable one, from which we derive the closed form solution on the optimal compression ratio, truncation threshold selection policy, and resource allocation strategy. We further introduce a heuristic algorithm with low complexity, leveraging insights from the structure of the optimal solution. Simulation results demonstrate that both the proposed optimal algorithm and the heuristic algorithm significantly reduce end-to-end latency. Notably, the proposed heuristic algorithm achieves nearly the same performance to the optimal solution but with considerably lower computational complexity.