How do we know black dwarfs exist?
Black dwarfs are theoretical objects. It is unlikely that any exist and we can't be sure when any will exist.
A black dwarf is based on a theory that white dwarf stars will eventually cool down to the point where they no longer emit light.
There are various theories on how long it will take for a white dwarf to cool down to a black dwarf. Theories give figures of over 100,000 times the existing age of the Universe for this to happen. So, the Universe is probably far too young for any black dwarfs to have formed.