Geometric foundation models show promise in 3D reconstruction, yet their progress is severely constrained by the scarcity of diverse, large-scale 3D annotations. While Internet videos offer virtually unlimited raw data, utilizing them as a scaling source for geometric learning is challenging due to the absence of ground-truth geometry and the presence of observational noise. To address this, we propose SAGE, a framework for Scalable Adaptation of GEometric foundation models from raw video streams. SAGE leverages a hierarchical mining pipeline to transform videos into training trajectories and hybrid supervision: (1) Informative training trajectory selection; (2) Sparse Geometric Anchoring via SfM point clouds for global structural guidance; and (3) Dense Differentiable Consistency via 3D Gaussian rendering for multi-view constraints. To prevent catastrophic forgetting, we introduce a regularization strategy using anchor data. Extensive experiments show that SAGE significantly enhances zero-shot generalization, reducing Chamfer Distance by 20-42% on unseen benchmarks (7Scenes, TUM-RGBD, Matterport3D) compared to state-of-the-art baselines. To our knowledge, SAGE pioneers the adaptation of geometric foundation models via Internet video, establishing a scalable paradigm for general-purpose 3D learning.