If it’s only on the open string, I’d start with the possibility that it’s the nut. Either it’s too low and the string is vibrating up against the 1st fret, or the slot is too wide on the fretboard side of the groove and the string is vibrating inside the slot.
Fret the string between the 2nd and 3rd fret with your right hand. Then press the same string between the nut and the 1st fret. If the string moves, then the slot depth isn’t the problem. If the string is already touching the first fret before the press it with your left hand, the slot is too deep.