Alan Guth and a host of others have proposed that the Big Bang / Universe could have resulted from a Quantum Fluctuation. No Supernatural agent required. Matter spontaneously pops into and out of existence all the time, as long as the net energy is zero and the time is short enough.
Of course he did. Allan guth was originally a particle physicist.
Inflationary cosmology, indeed suggests a solution to the horizon, homogeneity and flatness problems -- space simply expanded a couple of thousand times the speed of light. That explains a universe that is in thermodynamic contact everywhere plus it eliminates horizons. At some point, inflation stops and the universe expands at the rate we are observing presently.
What no one bothered to tell you is that such a thing is a bit contrived. You need to fine tune the initial conditions of the universe first. Next, you need omega to be very close to the critical density (in the order of 10^-50) for 13 billion years -- a tightrope act of cosmic proportions.
Now, while that is possible, it certainly isn't probable -- in much the same way that it is possible for you to hit the jackpot in any lottery but you do not go about your life as if you are going to, tomorrow. And the odds that inflation has anything to do with the truth is roughly equivalent to you hitting that jackpot a couple of weeks straight.
Oh, and it fails completely with the lambda problem.