I will hazard a guess that this is the short story "What Continues, What Fails" (1991) by <PERSON>. It's not a perfect match -- the female protagonist is part of a research team that is observing collisions of micro-black holes with a bigger one in order to observe things inside the bigger one, vs. waiting for one to collapse -- but the theme of universes spawning black holes which yield similar universes is a major focus.
A quote, describing how it is possible to see inside of black holes:
Tides tugged at the camera, suspended between, and at the fibre-thin cable leading from the camera to her recorders. Peering into one of those pits of blackness, the mini-telescope saw nothing. That was only natural.
Nothing could escape from inside a black hole.
A special kind of nothing, though. Nothing that had formerly been light, before being stretched down to true nothingness in the act of climbing that steep slope.
The two funnels merged closer still. The microscopic black balls drew nearer.
Light trying to escape a black hole is reddened to nonexistence. Nevertheless, virtual light can theoretically escape one nought, only to be sucked into the other. There it starts blue-shifting exponentially, as gravity yanks it down again. Between one event horizon and the other, the light doesn't "officially" exist. Not in the limiting case. Yet ideally, there should be a flow.
They had not believed her on Kalimarn. Until one day she showed them it was possible, for the narrowest of instants, to tap the virtual stream. 73
To squeeze between the red-shifted and blue-shifted segments. To catch the briefest glimpse --
And another, describing the creation of a "boring" universe in the lab:
Instants after the nought's formation, inflation had turned it into a macrocosm. A fiery ball of plasma exploding in its own context, in a reference frame whose dimensions were all perpendicular to those <PERSON> knew. Within that frame, a wheel of time marked out events, just as it did in <PERSON>'s universe -- only vastly speeded up from her point of view.
Energy -- or something like what she'd been taught to call "energy" -- drove the expansion, and traded forms with substances that might vaguely be called "matter." Forces crudely akin to electromagnetism and gravity contested over nascent particles that in coarse ways resembled quarks and leptons. Larger concatenations tried awkwardly to form.
But there was no rhythm, no symmetry. The untuned orchestra could not decide what score to play. There was no melody.
In the speeded-up reference frame of the construct-cosmos, her sampling probe had caught evolution of a coarse kind. Like a pseudo-life fabrication too long out of the vat, the universe <PERSON> had set out to create lurched toward dissipation. The snapshot showed no heavy elements, no stars, no possibility of self-awareness. How could there be? All the rules were wrong.
And one more, describing the "chain of universes" idea:
As DNA coded for success in life-forms, so did rules of nature -- fields and potentials, the finely balanced constants -- carry through from generation to generation of universes, changing subtly, varying to some degree, but above all programmed to prosper.
Black holes are eggs. That was the facile metaphor. Just as eggs carry forward little more than chromosomes, yet bring about effective chickens, all a singularity has to carry through is rules. All that follows is but consequence.
The implications were satisfying.
There is no mystery where we come from. Those cosmos whose traits lead to forming stars of the right kind -- stars which go supernova, then collapse into great noughts -- those are the cosmos which have "young." Young that carry on those traits, or else have no offspring of their own. 73