Extending humanoid traversal to open-world human environments is essential for real-world deployment but remains challenging. The robot must use vision to ensure safe and reliable foot placement on heterogeneous terrain under highly dynamic motion, while producing coordinated, natural whole-body behaviors. We propose SSR, an efficient end-to-end framework for egocentric vision-based humanoid traversal that jointly learns these capabilities. SSR introduces imagined foothold guidance, which learns to model forthcoming swing-foot contacts and support to guide pre-touchdown swings toward stable regions, reducing edge slips. It further employs a compact equivariant latent-space symmetry augmentation to efficiently induce bilateral coordination under high-dimensional visual observations, together with terrain-specific multi-discriminator motion priors that preserve human-like behavior across scenes. Extensive experiments show that SSR achieves safe, stable, and high-quality locomotion on diverse real-world terrains, including stairs with varied structures and extreme challenges such as wide gaps and high platforms, while enabling reliable long-horizon traversal in open outdoor environments.