From our point of view, no object can fall into a black hole in finite time. The object will seem to be more and more red-shifted to us, but it will never quite pass the schwarzschild-radius / event horizon. (Of course the time frame of the falling object is another thing, but we are well away from any direct effects of black holes on us)
Having said that, how can black holes come to existence? As soon as there would be a schwarzschild radius, nothing can cross it. To me this seems like a chicken-and-egg problem, so no black holes can possibly exist.
Obviously the black holes in our universe do not seem to be aware of this, so what am I missing?
Thanks in advance :-)