To the less well acquainted, inflation theory seems like a rather far fetched proposal. It makes very specific claims about the earliest moments of the universe, without being explainable in terms of well established physical theories, e.g. QFT or GR (correct me if I'm wrong). Specifically, it suggests rapid expansion of space in the first $\sim 10^{-33}$ seconds after the big bang. That is a very very short time, billions of years ago, to make such a strong claim about a large, formative event of our universe.
I understand there exists evidence ( such as large scale inhomogeneity ), but couldn't this be explained with a simpler model? Are there competing theories that also explain evidence used to support expansion theory?
In short, help a skeptical non-cosmologist understand why this theory is so strongly supported.