Self-supervised pre-training has driven rapid progress in foundation models for language, 2D images, and video, yet remains largely unexplored for learning 3D-aware representations from multi-view images. In this paper, we present E-RayZer, a self-supervised 3D vision model that learns geometrically grounded representations directly from unlabeled images. Unlike prior self-supervised methods such as RayZer, which infer 3D indirectly through latent-space view synthesis, E-RayZer operates directly in 3D space, performing self-supervised 3D reconstruction with Explicit geometry. This formulation eliminates shortcut solutions and yields representations that are 3D-aware. To ensure convergence and scalability, we introduce a fine-grained learning curriculum that organizes training from easy to hard samples and harmonizes heterogeneous data sources without any supervision. Experiments show that E-RayZer significantly outperforms RayZer on pose estimation and matches or sometimes surpasses fully supervised reconstruction models such as VGGT. Furthermore, its learned representations outperform leading visual pre-training models (e.g., DINOv3, CroCo v2, VideoMAE V2, and RayZer) on 3D downstream tasks, establishing E-RayZer as a promising paradigm for spatial visual pre-training.