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Hydrogen plays a major role as a low-carbon energy solution for global energy transition, but its low volumetric energy density makes underground hydrogen storage (UHS) in geological formations the only viable solution for meeting large-scale demand. Passive continental margins host thick Cenozoic successions and are located adjacent to many coastal demand centres, yet their UHS potential is hard to assess where subsurface data are limited. Here, using an open-source landscape evolution code, pyBadlands, we examine how Cenozoic sea-level changes influence passive-margin stratigraphic architecture, focusing on the greenhouse–icehouse transition at around 34 million years ago. Our models of the Hunter margin offshore New South Wales (Australia), an area transitioning from fossil fuel dependence to renewable energy, reveal two main depositional styles. Greenhouse intervals dominated by longer sea-level cycles favour the development of thicker (up to 50 m), laterally progradational packages, aligning with high-capacity reservoirs. In contrast, icehouse intervals marked by higher-frequency oscillations generate more vertically stacked, thinner stratigraphic units, which are more suitable for composite multi-layer sealing systems. The Eocene–Oligocene transition emerges as a potential key boundary separating these different depositional regimes. These contrasting architectures indicate that passive margin successions hosting both greenhouse thick reservoir packages and overlying icehouse multi-layer seal intervals can represent highly prospective configurations for UHS, thus providing storage capacity and containment integrity. However, favourable reservoir–seal architecture alone does not ensure UHS feasibility due to hydrogen’s high mobility, which can lead to vertical migration and leakage. Therefore, we applied a vertical mobility model to a representative offshore exploration well in the same region. Our results reveal a pronounced contrast in vertical velocity between potential reservoir and seal units, with the most favourable configurations observed in the deepest Cenozoic intervals: thick sandstone packages display high hydrogen mobility (~68 m/day), supporting high injection rates, whereas the immediately overlying laminated shale interval exhibits reduced vertical velocity (~0.02 m/day), ensuring effective containment capacity. These results demonstrate how paleoclimate-driven stratigraphic variability controls the distribution and performance of candidate hydrogen storage sites. By combining landscape evolution modelling with vertical mobility analysis, this work offers a predictive framework for assessing subsurface storage potential in data-limited passive margin settings, ultimately supporting more informed site selection and enhanced risk characterisation for UHS deployment along passive margins.