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We only knew to look for black holes because the physics predicted their existence.
The size of the event horizon is a clue to the size of the object creating it. First created by the collapse of a massive star
Definition: A singularity is any point, line, or surface of geodesic incompleteness.
What a singularity is NOT
The singularity is NOT the black hole. The existence of the singularity is implied by Singularity theorems in classical GR, but it is not the black hole, a black hole loosely being any region of spacetime hidden behind a horizon.
A singularity is NOT a massive lump of matter that's been squished into an infinitely dense point.
A singularity is NOT a place that even exists within spacetime but rather it is better described as an edge of the spacetime itself
Also, if the holographic principle holds true then another reason that matter can't be packed into an infinitely small volume is that matter can't be packed into a volume smaller than the volume enclosed by its own event horizon
