"Do black holes actually exist? Most physicists believe they do, basing their views on a growing body of observations. In fact, present theories of how the cosmos began rest in part on Einstein's work and predict the existence of both singularities and the black holes that contain them. Yet Einstein himself vigorously denied their reality, believing, as did most of his contemporaries, that black holes were a mere mathematical curiosity. He died in 1955, before the term "black hole" was coined or understood and observational evidence for black holes began to mount."
As you can see, they have growing evidence that black holes DO exhist, but they do NOT actually have complete proof. After all. How do you measure and prove something exhists when you can't even see it? When they tell you to believe something exhists without proof, it is called faith, and religion has a market on that.