So long as the Airport Express is running, there will be taxis coming into HK Station to pick up. It's in the CBD (easier to find a fare there) and many drivers would prefer to pick up arriving travellers than the drunks in Lan Kwai Fong (although that time might be a bit early for them to roll out). It's usually when it's raining they are scarce.
You get off the train, go through the ticket barrier and the taxi lines are right in front of you. Most people head for Lines 1 or 2, but there are people outside guiding the taxis to the next line, so it goes 1st taxi to Line 1, 2nd taxi to Line 2, etc. This can mean the queue Line 4 (of 4) goes faster because there are more people in Lines 1 and 2.
So if you have one of your party dash to Line 4 or 3, while the rest deal with the luggage, you might be out pretty quick.