When did it take place, and what was the cause of the first back hole in the universe? Does this time precede stars collapsing as a result of old age?
We don't know for sure.
It is possible that random fluctuations in the density of matter of the early universe created black holes that could be much smaller than regular black holes formed by stellar collapse. These would have formed in the moments after the big bang.
Otherwise the first stars formed about 400 million years after the big bang, and some of these could form black holes after their (short) lives. Stars over 250 solar masses (which could form in the early universe) would produce large black holes when they collapsed.