Errrr, from where ??

CX has flights that land at HKIA around 5:30 AM but I don't think that's OP's question

Presumably from within HK island or Kowloon side, from within town at your place of stay / hotel, etc. - taxi is the obvious & hotel front desk will be more than happy to arrange for one, usually - you can find one in front or flag one down. Metered fare w. a small tip should come to less than $50 USD or under $400 HKD depending on the origin. It would be faster in the early morning hours, leaving around 4:45 to 5 AM to get there by 6 AM.

You can also ride one of the overnight CityBus that continues to run late night/early morning, essentially 24/7 depending on your whereabouts - use the Point to Point search function and it will show you what's available, etc. - it's economical but allow extra travel time as it will be stopping on the designated route - upwards of 60 to 90 minutes travel time to get to HKIA. http://www.nwstbus.com.hk/routes/air...ute/index.aspx

N11 Bus departing Central at 4:20 AM & if you are referring to the Grand Hyatt, closest stop is on Hennessy Road & Luard Road (stop #8) a few minutes later - no later than 4:30 AM should get you there around 5:45 AM.