Are we able to achieve Xian airport from the downtown early morning (till 6am) by Bus or Subway?

Well, the earliest schedule of shuttle bus Xishaomen Line is 05:00. And shuttle bus Railway Station Line starts from 06:00.
Generally speaking, you need to arrive at the airport 2 hours in advance. So you'd better to take a taxi from downtown area to the destination directly. The cab fare is CNY130-150 in the early morning.