Serverless computing faces growing memory pressure due to emerging workloads such as machine learning inference and stateful caching. While the adoption of Compute Express Link (CXL) memory provides scalable capacity, naive or runtime memory tiering often fails in ephemeral, latency-sensitive serverless environments, resulting in hot-page misplacement and significant performance degradation. We propose PTS, a snapshot-guided proactive memory tiering framework specifically designed for serverless platforms. Instead of relying on costly runtime page migrations, PTS performs page-level heat classification offline and embeds heat metadata directly into function snapshots. At invocation, PTS proactively allocates hot pages to DRAM and cold pages to CXL memory, ensuring all pages are correctly placed before execution begins. Moreover, PTS incorporates a heat-aware scheduler that minimizes DRAM contention and balances hot data distribution across nodes. Our evaluation with diverse serverless benchmarks shows that PTS reduces latency by 10–44% compared to existing memory tiering approaches. These results underscore the value of pre-tiering in serverless systems and demonstrate that PTS significantly outperforms current tiering mechanisms in both performance and resource efficiency.