I think one key to scientific advance has been the changing attitude to religion. Before then the scientific community, as well as society in general, was happy to accept that most events and phenomena were "The work of God". I think fledgling scientists started to look at the world differently when they realised that there might be other explanations for thing other than them being the will of God. That was the start of the Renaissance - or 'rebirth' - the rediscovery of old ideas and science.
Good examples might be Galileo rediscovering the fact that the Earth orbits the sun and isn't the centre of the universe. Fossils were realised to be ancient creatures and not relic of the Flood, geology developed when people realised the Earth must be much older than previously thought, volcanoes, earthquakes and storms weren't the anger of God etc. Medicine developed the same way, astrophysics etc.
That point in time is vague as it took a long time to overcome the religious mindset which was 1500 years old. The Renaissance was the point when science started to advance again and rediscover much of the knowledge that was known to the Greeks, Romans and Arabs.
Hope that helps and makes sense Jomifl!