I don't think there is a single answer to that question. One answer is that diffraction limits the resolution of a 56 mm objective to 6 mm at about 550 yds. Atmospheric turbulence-induced blur will reduce the range to a value that depends on air and ground temperature, height above the ground, etc.
However, if the bullet hole has high contrast, it can be visible at much longer ranges, even with turbulence. In the same way that we can "see" stars that are millions of light years away, we can visually detect and locate a bright or dark spot on a paper target at a range well beyond the limit of resolution.
The answer to your question depends on the caliber of the bullet, the color and reflectivity of the target, atmospheric and illumination conditions, the reflectivity of the background behind the target, and the vision acuity of the observer.