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The research on tasks involving differentially private data stream releases has traditionally centered around real-time scenarios. However, not all data streams inherently demand real-time releases, and achieving such releases is challenging due to network latency and processing constraints in practical settings. We delve into the advantages of introducing a delay time in stream releases. Concentrating on the event-level privacy setting, we discover that incorporating a delay can overcome limitations faced by current approaches, thereby unlocking substantial potential for improving accuracy. Building on these insights, we developed a framework for data stream releases that allows for delays. Capitalizing on data similarity and relative order characteristics, we devised two optimization strategies, group-based and order-based optimizations, to aid in reducing the added noise and post-processing of noisy data. Additionally, we introduce a novel sensitivity truncation mechanism, significantly further reducing the amount of introduced noise. Our comprehensive experimental results demonstrate that, on a data stream of length $18,319$, allowing a delay of $10$ timestamps enables the proposed approaches to achieve a remarkable up to a $30times$ improvement in accuracy compared to baseline methods. Our code is open-sourced.