Single-source open-domain generalization (SS-ODG) addresses the challenge of labeled source domains with supervision during training and unlabeled novel target domains during testing. The target domain includes both known classes from the source domain and samples from previously unseen classes. Existing techniques for SS-ODG primarily focus on calibrating source-domain classifiers to identify open samples in the target domain. However, these methods struggle with visually fine-grained open-closed data, often misclassifying open samples as closed-set classes. Moreover, relying solely on a single source domain restricts the model's ability to generalize. To overcome these limitations, we propose a novel framework called SODG-Net that simultaneously synthesizes novel domains and generates pseudo-open samples using a learning-based objective, in contrast to the ad-hoc mixing strategies commonly found in the literature. Our approach enhances generalization by diversifying the styles of known class samples using a novel metric criterion and generates diverse pseudo-open samples to train a unified and confident multi-class classifier capable of handling both open and closed-set data. Extensive experimental evaluations conducted on multiple benchmarks consistently demonstrate the superior performance of SODG-Net compared to the literature.