Ok, here is something to think about, when accelerating from a dead stop, are you on uneven terrain? What I mean is it possible one wheel is leaving the ground enough to cause wheel spin and have ESP kick in? In my experience the only thing that really ever caused this supposed death lag was described above. If I know the area I am pulling out of is uneven enough to possibly cause wheel spin, I turn ESP off. This way the wheel spins a little, but the car it still being moved by the other 3 wheels.
If that is not the case then you need to do a reset of the adaptive throttle. You don't need the VAG for this. Just go out to the Treg put the key in the ignition and hold the accelerator the whole way to the floor. Then turn the key to on, do not I repeat do not start the vehical at all. You just want the accessory mode. Hold the pedal to the floor for about 10 seconds then turn the car off. Next time you drive it the car will learn your way of driving.