The concept of optimality in geostatistical inversion is traditionally rooted in a Euclidean framework, which often oversimplifies complex spatial relationships in geological structures, potentially leading to suboptimal representations of subsurface properties. This study challenges this conventional approach by introducing manifold embedding, a method that incorporates non-Euclidean geometries to better capture the complex and non-stationary nature of geological structures. Through the application of Kalman filtering (KF) and geostatistical principal component adaptation evolution strategy (GPCA-ES), we explore how different geometric frameworks influence the outcomes of hydraulic conductivity estimations in a synthetic aquifer. Our results demonstrate that while Euclidean-based methods may provide a single “optimal” solution, they do not necessarily yield the most geologically accurate models. By incorporating manifold geometries, we reveal a broader range of plausible subsurface interpretations, all of which produce similar hydraulic responses at observation points. This finding highlights the limitations of relying solely on Euclidean assumptions and challenges the conventional notion of a unique optimal solution in hydrogeological inverse problems. The study underscores the importance of adopting a more comprehensive geometric perspective in hydrogeological modeling, offering a pathway to more geologically meaningful and potentially more reliable subsurface characterizations. These findings advocate for a fundamental shift in the approach to geostatistical inversion, emphasizing the need to move beyond traditional optimality criteria and toward a more nuanced understanding of subsurface environments that acknowledges the inherent complexity and non-uniqueness of geological structures.