Non-IID data and partial participation induce client drift and inconsistent local optima in federated learning, causing unstable convergence and accuracy loss. We present FedSSG, a stochastic sampling-guided, history-aware drift alignment method. FedSSG maintains a per-client drift memory that accumulates local model differences as a lightweight sketch of historical gradients; crucially, it gates both the memory update and the local alignment term by a smooth function of the observed/expected participation ratio (a phase-by-expectation signal derived from the server sampler). This statistically grounded gate stays weak and smooth when sampling noise dominates early, then strengthens once participation statistics stabilize, contracting the local-global gap without extra communication. Across CIFAR-10/100 with 100/500 clients and 2-15 percent participation, FedSSG consistently outperforms strong drift-aware baselines and accelerates convergence; on our benchmarks it improves test accuracy by up to a few points (e.g., about +0.9 on CIFAR-10 and about +2.7 on CIFAR-100 on average over the top-2 baseline) and yields about 4.5x faster target-accuracy convergence on average. The method adds only O(d) client memory and a constant-time gate, and degrades gracefully to a mild regularizer under near-IID or uniform sampling. FedSSG shows that sampling statistics can be turned into a principled, history-aware phase control to stabilize and speed up federated training.