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Subsea permafrost stability is the key to whether pre-performed methane sequestered in hydrate deposits escapes to the overlying strata. By making use of the 1D numerical modeling and field data, we analyze the capabilities of the time-domain (transient) electromagnetic method (TDEM) when being applied for subsea permafrost mapping, and study the effect of the background resistivity structure on the inversion models’ accuracy for a series of settings typical for the East Siberian Arctic Shelf—the broadest and shallowest shelf in the world ocean, which represents more than 70% of the subsea permafrost. The synthetic response analysis included the construction of a series of resistivity models corresponding to different settings (presence/absence of ice-bonded permafrost layer, different position of its top and bottom boundaries, different width and thickness of thawed bodies or taliks, variable seawater depth and its resistivity), and calculation of synthetic apparent resistivity responses used to assess their sensitivity to changes in the target parameters of the resistivity structure. This was followed by regularized inversion of synthetic responses and comparing resulting models with original (true) ones, which allowed us to understand the possible uncertainties in the geometry and resistivity of the reconstructed permafrost layer, depending on seawater depth and unfrozen layer thickness, as well as confirm the overall efficacy of TDEM technology for the subsea permafrost imaging. That is crucially important for understanding the current state of the subsea permafrost-hydrate system and possible future dynamics.