In this work, we design SnapBPF, an eBPF-based snapshot prefetching mechanism, targeting VM-sandboxed serverless functions, which enables the efficient capture and prefetching of function working sets in kernel-space. SnapBPF deduplicates function working sets in memory and obviates the need for separately serializing them on disk. We complement SnapBPF with a lightweight paravirtualized interface to efficiently handle VM-sandbox memory allocations without requiring any snapshot pre-processing. Our evaluation shows that SnapBPF is able to match and improve state-ofthe-art performance with regard to i) function invocation latency and ii) memory usage for concurrent function invocations, without separately serializing working sets on disk or requiring any preemptive snapshot scanning.