Hi, I am staying next month in Hong Kong

The easiest way from HK to SZ is to take a ferry from Futian Port, Luohu Port or Shekou Port.

There is only a ferry terminal at Shekou port, not at the other locations. From shekou ferry terminal you can take a bus or a taxi to the S airport. Or you can take a shuttle to the metro station, ride line 2 to houhai station, and transfer to the express line 11 to the SZ airport.

It is much easier to take a coach directly from HK airport (lower level ground transporation) directly to the Shenzhen airport.

One other comment, having noticed how early is your flight from Shenzhen (0600). There is no convenient way to cross the border that early and make your flight on time. Only one border crossing is open 24 hours, and the metro system does not run so early. I strongly recommend you cross to Shenzhen the day before and spend the night near the airport.