The type of lithosphere subducted between India and Tibet since the Paleocene remains controversial; it has been suggested to be either entirely continental, oceanic, or a mixture of the two. As the subduction history of this lost lithosphere strongly shaped Tibetan intraplate tectonism, we attempt to further constrain its nature and density structure with numerical models that aim to reproduce the observed history of magmatism and crustal thickening in addition to present-day plateau properties between 83˚E and 88˚E. By matching time-evolving geological patterns, here we show that Tibetan tectonism away from the Himalayan syntaxis is consistent with the initial indentation of a craton-like terrane at 55±5 Ma, followed by a buoyant tectonic plate with a thin crust, e.g., a broad continental margin (Himalandia). This new geodynamic scenario can explain the seemingly contradictory observations that had led to competing hypotheses like the subduction of Greater India versus largely oceanic subduction prior to Indian indentation. This work has been partially published in Geophysical Research Letters (Liu et al., 2021) and Nature Communications (Liu et al., 2023, in press).