This paper introduces Domain Generalization Sharpness-Aware Minimization Model-Agnostic Meta-Learning (DGS-MAML), a novel meta-learning algorithm designed to generalize across tasks with limited training data. DGS-MAML combines gradient matching with sharpness-aware minimization in a bi-level optimization framework to enhance model adaptability and robustness. We support our method with theoretical analysis using PAC-Bayes and convergence guarantees. Experimental results on benchmark datasets show that DGS-MAML outperforms existing approaches in terms of accuracy and generalization. The proposed method is particularly useful for scenarios requiring few-shot learning and quick adaptation, and the source code is publicly available at GitHub.