#####Science certainly narrows down the range of possible gods. Science, for example, disproves a god who created the world in 6 days 6000 years ago. In fact, since science rules out particular divine possibilities, one could say science favors distant, noninterventionist deities.#####
Miracles don't leave traces, so science can't disprove the existence of any God, including one who created the world 6,000 years ago. I'm not a YEC, but either God exists or He doesn't. If He exists, He isn't limited by Dawkins' imagined rules about how God would have to operate.
Sure it can.
I'm not referring to a mathematical standard of proof here; just the same proof we'd use in a legal case or otherwise in everyday life: proof beyond reasonable doubt. I don't need purity - 99.44% will do fine.
In that case there is massive evidence from astronomy, geochemistry, biology, and so on that the earth is more than 6000 years old. In fact, only Omphalism could possibly reconcile the evidence with the science. Since reasonable people discard Omphalism, the earth is far older than 6000 years, beyond reasonable doubt. Therefore, the specific god that allegedly created the earth at that time is disproven. QED.