"Why did the universe seem to start from a condition of low entropy?"

I'm confused here. If we don't go with a big universe and instead just say that our observable universe is the whole thing, then tracing back time we find that it began with a very small volume. While it's true that such a system wold necessarily have low entropy, that's largely because small volume = not many different places to put things.

Alternative hypothesis: The universe began in a state of maximal entropy. This maximum value was "low" compared to present day because the early universe was small. As the universe expands, its maximum entropy grows. Its realized entropy also grows, just not as fast as its maximal entropy.