Have you read Ranger's post on how to launch a C6? Here it is:
Before doing launches at the track, you need to turn off Traction Control.
You want the setting that allows wheel spin but retain Active Handling or Stability Control.
In a C5 Corvette you want to be in Competitive Driving mode.
In a C6 Corvette you want to be in Traction System Off mode.
Other platforms will have different descriptive settings.
Lower your stock rear tire pressure to about 25 psi (hot).
The exact pressure varies by platform, tire model, and track conditions. The goal is to remove 15-20% of the air, again "hot."
This will increase the size of the tire's contact patch with the launch surface and cushion the shock to the drive line on launch and shifts.
I recommend a launch procedure with three deliberate elements that are inter-related and must be coordinated.
(1) the launch rpm
(2) the clutch release
(3) the throttle squeeze
Hold the launch rpm and then quickly but smoothly release the clutch with full engagement occurring over the first 3-10 feet of forward movement, depending on conditions.
Don't feed more throttle until the tires are hooked.
Then and only then, squeeze the throttle progressively to the floor.
Drag radials will take throttle quicker than stock tires but even on DRs it's still a "squeezing" action rather that just "hammering it" to the floor in one movement.
The goal is getting a bit of wheel spin which gives way to a rapid rise in engine rpm, rather than a bog. If it bogs, raise the launch rpm a few hundred on the next time. If it spins too much, lower the launch rpm a few hundred on the next pass.
Finally, it takes seat time and passes to embed the techniques in muscle memory and learn to read what surface conditions dictate on any particular day.
I urge avoiding the classic launch error: engaging the clutch and hammering the throttle simultaneously.