Answering Select-Join-Aggregate queries with DP is a fundamental problem with important applications in various domains. The current SOTA methods ensure user-level DP (i.e., the adversary cannot infer the presence or absence of any given individual user with high confidence) and achieve instance-optimal accuracy on the query results. However, these solutions involve solving expensive optimization programs, which may incur prohibitive computational overhead for large databases. One promising direction to achieve scalability is through sampling, which provides a tunable trade-off between result utility and computational costs. However, applying sampling to differentially private SJA processing is a challenge for two reasons. First, it is unclear what to sample, in order to achieve the best accuracy within a given computational budget. Second, prior solutions were not designed with sampling in mind, and their mathematical tool chains are not sampling-friendly. To our knowledge, the only known solution that applies sampling to private SJA processing is S&E, a recent proposal that (i) samples users and (ii) combines sampling directly with existing solutions to enforce DP. We show that both are suboptimal designs; consequently, even with a relatively high sample rate, the error incurred by S&E can be 10x higher than the underlying DP mechanism without sampling. Motivated by this, we propose Differentially Private Sampling for Scale (DP-S4S), a novel mechanism that addresses the above challenges by (i) sampling aggregation units instead of users, and (ii) laying the mathematical foundation for SJA processing under RDP, which composes more easily with sampling. Further, DP-S4S can answer both scalar and vector SJA queries. Extensive experiments on real data demonstrate that DP-S4S enables scalable SJA processing on large datasets under user-level DP, while maintaining high result utility.