Abstract: As next-generation wireless networks evolve toward integrated sensing and communication (ISAC), radio simultaneous localization and mapping (radio SLAM) has emerged as a promising approach for joint user localization and environmental reconstruction by exploiting high-resolution channel measurements enabled by millimeter-wave (mmWave) bandwidth and massive multiple-input multiple-output (MIMO) systems. This paper focuses on a bistatic downlink snapshot radio SLAM scenario, where the base station state is known and the user equipment state is unknown, and investigates how to achieve robust localization and path-type identification using a single channel measurement snapshot. In particular, snapshot radio SLAM performs sensing and localization using only a single channel snapshot, offering high responsiveness and low deployment complexity. However, existing snapshot radio SLAM methods generally require separate modeling of line-of-sight (LoS) and single-bounce non-line-of-sight (NLoS-1) paths, which in turn relies on prior LoS detection. Since prevailing LoS detection schemes are strongly dependent on path amplitude, uncertainties in amplitude modeling may lead to path misclassification and consequently degrade state estimation accuracy. To address this issue, this paper proposes a multipath amplitude-independent modeling and optimization method for robust snapshot radio SLAM. First, a unified geometric model is developed to jointly characterize the angular and delay constraints of LoS and NLoS-1 paths without explicitly introducing scatterer information. This removes the need for initial LoS detection and enables simultaneous user equipment (UE) state estimation and inlier identification. Then, an iterative refinement scheme based on model selection is introduced to further improve UE state estimation while performing LoS detection. Simulation results show that the proposed method eliminates the dependence on amplitude modeling and achieves stable and accurate UE state estimation under both LoS and NLoS conditions. In particular, it demonstrates substantially improved robustness in challenging scenarios involving NLoS propagation, path-loss model mismatch, and high-noise conditions.