Cross-view geo-localization (CVGL) matches query images ($\textit{e.g.}$, drone) to geographically corresponding opposite-view imagery ($\textit{e.g.}$, satellite). While supervised methods achieve strong performance, their reliance on extensive pairwise annotations limits scalability. Unsupervised alternatives avoid annotation costs but suffer from noisy pseudo-labels due to intrinsic cross-view domain gaps. To address these limitations, we propose $\textit{UniABG}$, a novel dual-stage unsupervised cross-view geo-localization framework integrating adversarial view bridging with graph-based correspondence calibration. Our approach first employs View-Aware Adversarial Bridging (VAAB) to model view-invariant features and enhance pseudo-label robustness. Subsequently, Heterogeneous Graph Filtering Calibration (HGFC) refines cross-view associations by constructing dual inter-view structure graphs, achieving reliable view correspondence. Extensive experiments demonstrate state-of-the-art unsupervised performance, showing that UniABG improves Satellite $\rightarrow$ Drone AP by +10.63\% on University-1652 and +16.73\% on SUES-200, even surpassing supervised baselines. Code will be released upon publication.