Black holes were first seriously theorized in the early 20th century, but it took many decades before one could be observed; depending on your definition of "observe," this may have occurred as early as the 1998 research theorizing that only a black hole could explain the orbits of objects around Sagittarius A*, or as late as the 2019 direct imaging of M87*. And these observations were achieved by astronomers laboring under the consensus that black holes probably exist.
Assuming that scientific/engineering research progressed at about the same pace (up until this discovery, which would fork its development significantly), what are the closest and/or furthest locations where a black hole could be located such that it will be observed before it would be theorized in the 20th century, and how early would that observation happen? "Observe" being defined as "collect observations sufficient to convince astronomers that an object defying understood physics exists at the specific location of a real black hole," so something like the Sag A* research would count.
Both the upper and lower limit on distance are interesting questions - a black hole as nearby as the moon would need to be small and lack an incandescent accretion disk in order to not disrupt life on Earth, which might make its optical lensing effect too small to observe with pre-20th century telescopes. Black holes further away can be larger and have incandescent accretion disks without cooking Earth, but they're harder to observe and you would need to be able to tell it apart from a normal star based on historical observation - just being bright isn't sufficient.