One class of single-field inflationary models compatible with the recently-conjectured Swampland criteria would be those in which a Hubble slow-roll parameter is not the same as $\epsilon_ \sim (V’/V)^2$. However, a roadblock for these models (with a convex potential) lie in the unacceptably high tensor-to-scalar ratio, , generically predicted by them. In this work, illustrating through an explicit example, we point out that having a non-Bunch-Davies component to the initial state of cosmological perturbations makes the value of compatible with observations. In this way, we lay down a new path even for standard models of slow-roll inflation to be consistent with the Swampland criteria by invoking deviations from the Bunch-Davies initial state.

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