We present a complete and robust framework for non-singular bouncing cosmology in a closed universe (\(k=+1\)). The regularized field space metric \(g^S_{\chi\chi} = (1 + e^{-2\alpha\phi/M_{\rm Pl}})^{-1}\) is derived from fundamental boundary conditions, uniquely emerging as a sigmoid function. This enables a cosmological bounce at finite energy density, followed by 60+ e-folds of inflation without violating the Null Energy Condition. The model demonstrates exceptional robustness, with a 100% success rate across 16 orders of magnitude in initial conditions. The subsequent inflation naturally solves the flatness and anisotropy (BKL) problems. Observable predictions include the spectral index \(n_s \approx 0.967\) and tensor-to-scalar ratio \(r \approx 0.003\), which are universal (independent of \(\alpha\)) and in striking agreement with Planck 2018 data.