Old English soðian "show to be true," from soð "true" (see sooth). Sense of "quiet, comfort, mollify" is first recorded 1690s, via notion of "to assuage one by asserting that what he says is true" (i.e. to be a yes-man), a sense attested from 1560s (and compare Old English gesoð "a parasite, flatterer"). Meaning "reduce the intensity" (of a pain, etc.) is from 1711. Related: Soothed; soothing.
<a href="https://www.etymonline.com/word/soothing">Etymology of soothing by etymonline</a>
Harper, D. (n.d.). Etymology of soothing. Online Etymology Dictionary. Retrieved $(datetime), from https://www.etymonline.com/word/soothing