The Big Splat Theory proposes that two universes collided in an extra-dimensional superverse or multiverse 13.8 billion years ago and became the Big Bang. The collision had to be perfectly aligned three-dimensionally, analogous to parallel 2D planes, in order to produce the homogeneity that is seen in the universe today. Depicted here as membranes ("branes") are two universes in the multiverse ("The Incredible Bulk") aligned in such a way that a collision would produce the distribution of galaxies observed in our universe.There are several versions of the Big Bounce Theory, all of them involve a cycle of collapse and rebound. The Big Bang universe seen today is on the rebound from the prior bounce.
Lee Smolin calls his evolutionary model the Cosmological Natural Selection Theory. The idea is that there are countless universes being created, each coming from the white hole side of a black hole. Each bubble universe is born with a unique set of physical laws, some sets being more conducive to the creation of black holes than others. Only those universes with physical laws that result in black holes can reproduce. Baby universes tend to inherit physical laws that are similar to those of their parent universes. So, after countless generations of universes, the proportion of baby universe that produce black holes increases, ours being one of them. Black holes also play key roles in the formation of galaxies, increasing the odds that life will emerge. After sufficient numbers of universes are created, the odds that life emerges in one or another of them is high.
Roger Penrose has proposed the Conformal Cyclic Cosmology Theory, another cyclical idea that is often mistaken for a Big Bounce theory. After a Big Bang has expanded and cooled to thermal equilibrium and the last black hole has evaporated into radiation, the only stuff remaining would be gravitons, gluons, and photons. None of these particles have mass. Massless particles have no reference frame and therefore cannot cannot experience time or distance. One couldn't say that the universe has collapsed, only that space and distance would become meaningless. The universe would be the same as it was before the Big Bang with space and time undefined and therefore the equivalent of infinitely compressed, not by collapse, but by loss of spacetime definition. Then it would go through a phase change that becomes the next Big Bang cycle. It's sort of one continuous Big Bang with a cold blackout phase separating the hot phase that slowly cools during expansion. Penrose hopes to see evidentiary patterns in the Cosmic Background Radiation that support his theory.The Big Splat, Big Bounce, Conformal Cyclic Cosmology, and Cosmological Natural Selection theories are just several of many theories that attempt to explain what happened at and before the first moment of the Big Bang where the math of physics can't go. But they're just theories and nobody knows which, if any, is even directionally correct.
As for Genesis, its story begins with the earth already created, "without form, and void." (Gen 1:2) Since the Bible has no story for the beginning of the universe or the expansion called the Big Bang, there is no conflict.