According to the Guitar Guru column "Guitar Inlays - All About Those Fretboard Markers" on ledgernote.com,
Inlays on the modern guitar find their roots ... in the historic companies of Fender and Gibson. (Retrieved 22 Jan 2022)
And furthering the idea that these were the first uses of guitar inlay for fret-marking is this item from "Why Are There Dots on Guitar Fretboards? All About Guitar Inlays and Markers" on GuitarGearFinder.com (27 July 2020).
Classical guitars traditionally don’t have fretboard markers. (Retrieved 22 Jan 2022)
Inlay was most certainly used on earlier stringed instruments, including guitar, but as decoration rather than as fret markers. As one example of many, here is a late 17th-century guitar with fretboard inlay. Once can see clearly that the inlay was not measured to correspond to the fret placement.
(IMAGE SOURCE: Metropolitan Museum of Art)