practice, son... practice.
with control comes speed. control does not come from just going fast... that's how accidents and crashes happen. learn to control your bike and be comfortable with it first before you force yourself to push it beyond your current comfort level.
I suggest finding a nice open stretch of road with no cars and practice accelerating from a dead stop under the same conditions you describe. Try it as many different ways that you think will make a difference. In the end, you'll end up with a better understanding with how your bike runs when pushed to it's limits.
If I need to get from a dead stop to max speed in the least amount of time, I make the shift at redline.
I never redline in first gear though. I think of first gear as more of a rolling entry into second gear because the engine simply revs through first in a blink of an eye.