In smart manufacturing, the injection molding industry faces a “data scarce environment” due to prohibitive physical trial costs. Processing recycled polypropylene (rPP) exacerbates this challenge, as traditional response surface methodology (RSM) fails to capture complex non-linear rheological behaviors induced by material variability. This study proposes a “domain-knowledge guided data augmentation framework,” integrating Taguchi experimental data (L₂₅) with Moldex3D digital twin simulations to construct a 300-sample hybrid dataset. A back-propagation neural network (BPNN) with L₂ regularization was employed for small-sample learning, providing a continuous differentiable physical mapping. To rigorously prevent neighborhood data leakage, the model was evaluated via a strict nested group-based 5-fold cross-validation. Particle swarm optimization (PSO) was coupled to overcome the local minima of gradient descent. Comparative analysis demonstrates that BPNN significantly outperforms both traditional RSM and a newly introduced Random Forest (RF) baseline, achieving a testing mean squared error (MSE) of 0.001 (±0.0002) and a testing R² of 0.95. PSO minimized the shrinkage rate to 3.079%, validated via Moldex3D digital twin simulation with a 0.19% relative error. Synergizing virtual–physical integration with robust neural computing enables superior process control precision in small-data regimes, offering small and medium-sized enterprises (SMEs) a cost-effective pathway for smart optimization.