This is a huge subject, covering a multitude of scientific disciplines.
First off, the processes that lead from the original Big Bang to life on Earth are known in pretty good detail.
* (-infinity) -> (Big Bang t0 : 12 billion years ago)
'Prior' to the Big Bang (which is not a useful descriptive term) only hypotheses exist - but they're good ones. They involve M-theory, branes, superstrings, a 10-D multiverse and similar weird stuff that is only thought to exist by some. Watch this space.
* (Big Bang t0) -> (Big Bang+(1e(-43)s) : 12 billion years ago)
The Instant of the Big Bang itself is also closed to 'normal' mathematical exploration at the moment. During this period - which is called a Planck Time, the smallest unit of time - the universe was less than a Plank Unit (the smallest unit of space) in size. All the math science has is broken for the duration: some numbers go to zero, others fly off to infinity. We haven't developed the tools to describe the situation.
But among the popular hypotheses being worked on is one in which the 'brane' (an N-dimensional sheet on which all normal particles exist as tiny loops of 'string') in which our universe was to exist received a massive injection of energy from a nearby explosion - caused by another brane colliding with an anti-brane.
This energy spill-over appears to have begun at a point, and was great enough to eventually become the entire universe as we see it today.
* (Big Bang+(1e(-43)s)) -> 5 Billion years ago.
Things improve mathematically after the first Planck instant: the zeroes and infinities become real numbers, and it's possible to find figures for temperature, mass and velocity. Observations confirm these figures.
From a point (ten-to-the-minus-43) seconds after the BB until now, the cosmological model hangs together well, and predicts things like the hydrogen/helium ratio and the Cosmic Microwave Background accurately. Matter condenses, stars form, galaxies form, planets form. Earth accretes, along with the rest of the Solar System, out of the dust-cloud spewed out by at least three nearby supernovae. This combination of physics, cosmogony, cosmology and math get us up to a warm, wet, anaerobic Earth.
* 5 billion years ago -> 4.5 billion years ago
Then there's a period of Abiogenesis, which can't be verified at present because billion-year experiments are hard to do. The biochemistry is sound, however, and each new set of data is yielding better results for the formation of biochemical goo on the planet, the first Replicator, and the first primitive cells.
* 4.5 billion years ago -> Now
Once you have a Replicator, evolution takes over, and builds up complexity and variation over the subsequent billions of years until we get to now - where the planet's dominant animals are beetles or bacteria, and the dominant species is grass.