Inflation in what era? There has to have been some inflation at some point, right, otherwise how could the very hot period that's considered to be right after the start of the universe be low entropy? Sure, maybe you could say there's no big bang and time runs the other way on the other side of that low entropy state, but there has to be some sort of low entropy state.
It could be that it is actually not low entropy, and there are some other processes that explain a recution in entropy at some scale. That is, maybe the second law of thermodynamics is not that universal.
That would be really weird. I'd be more willing to buy galaxies just coming into existence somehow in the gaps as the universe expands, as that at least drives the arrow of time consistently in the right direction.
The arrow of time can survive local entropy reduction, but probably not what you're talking about.
