The origins of hot Jupiters, giant planets with orbital periods shorter than about a week, remain mysterious. These planets are thought to have migrated inwards from larger orbital distances, but it remains unclear whether this migration occurred early-on, while the protoplanetary disk was present, or whether migration occurred tens of millions of years later via an alternative dynamical pathway. In this work, we leverage the observed distribution of misalignments between hot Jupiter orbits and the spin axes of their host stars, in order to place novel constraints upon the timing of hot Jupiter arrival in a selection of systems. Specifically, among hot Jupiters, large spin-orbit misalignments are common when the host star’s surface temperature exceeds 6000K, with cooler hosts exhibiting more aligned configurations. Coincidentally, stars below 6000K possess thick convective envelopes, which are subject to strong tidal dissipation that is lacking in their hotter counterparts. Thus, tidal dissipation stands as a likely mechanism for aligning cool stars with their hot Jupiter orbits. However, even hot stars begin their lives fully convective, only losing their convective envelopes after 10s of millions of years. In this presentation, we combine stellar evolution models with tidal theory to show that this early convective phase would have removed spin-orbit misalignments in a number of hot Jupiter systems known to nonetheless exhibit large misalignments. That is, we identify a sub-set of hot Jupiters that must have attained their close-in orbits later than the disk-hosting stage. Moreover, we highlight testable predictions for the theory of tidal obliquity erasure in terms of the relationship between stellar tilts and stellar metallicities. Cumulatively, we show that stellar obliquities serve as a critical and independent window into the migration history of hot Jupiters.