I will hazard a guess that this is the short story "What Continues, What Fails" (1991) by David Brin. 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
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
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. 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 Isola
knew. Within that frame, a wheel of time marked out events, just as it
did in Isola's universe -- only vastly speeded up from her point of
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
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 Isola
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.