Astronomy Question:

As far as we can tell, they do exist, yes. Whilst no one has directly seen a black hole, they are of course dark objects so light cannot be seen; the effects of them can be seen.

Specifically the massive gravitational field and its impact can be observed at the centre of galaxies where the orbits of stars and matter do all sorts of crazy things from the intense gravitational pulls, so objects that behave consistently with the behavior of black holes at the centre of galaxies have had their predictions confirmed, yes.