I don't know if Greek philosophy was uniquely advanced; I would suspect not, but I know nothing about Chinese philosophy.

Why did the Greeks get to sit down and philosophise? The simple (and, probably, simplistic) answer is that they were rich. Philosophy can't take place in a vacuum; you need to have considerable structure in order for it to take place. Greece had that, for whatever reasons you want to suppose.

The first Greek philosopher was a man named Thales of Miletus. The reason I mention him is because Miletus was a very rich trading town, and Thales was a bright young philosopher. When you have bright young(ish) men sitting around not having to work, they tend to find something with which to occupy themselves, and Thales started the philosophical tradition.

So, in summary:

1. Greece was wealthy.
2. Greece was socially/politically advanced
3. Philosophers tended to be wealthy, aristocratic men with no need to work.

Side note: not all Greek philosophy happened in Greece. Quite a few of the great philosophers came from Asia Minor or Italy, where there were Greek colonies (Pythagoras, or Heraclitus, for example, were both not Greek).

I hope this helps :)