Online order acceptance in cloud manufacturing faces heterogeneous and stochastic order streams with real-time arrivals. Manufacturers must dynamically trade off accepting current orders and reserving capacity for potential high-value orders to maximize long-term profit. This paper focuses on the perspective of manufacturers in cloud manufacturing, studying the problem of dynamic order acceptance with strategic waiting in a multi-machine parallel manufacturing system under random order arrivals. Existing studies largely rely on deterministic assumptions or myopic rules that fail to quantify the value of waiting; exact dynamic programming further suffers from the curse of dimensionality in large-scale settings. We propose a Feature-Driven Approximate Dynamic Programming (FD-ADP) approach that models strategic waiting through state-dependent value approximation using compressed resource–load–time features. Numerical experiments show that FD-ADP achieves about 93% of the theoretical optimum, is significantly more computationally efficient than dynamic programming, and yields higher profits than PSO and GA. Strategic waiting emerges under specific system states and yields the largest marginal profit gains at moderate customized-order arrival rates. The proposed framework offers an efficient and near-optimal solution for dynamic order acceptance under stochastic demand in cloud manufacturing.