It might be worth checking whether your R2 is working properly. Jump into the DS Survolt and go into cockpit cam. The steering wheel has a display in the center and on the upper left hand side of it is a meter that goes from 0-100. Hold down R2 and see if it actually goes to 100. If it doesn't, then your R2 is busted and the cars won't accelerate properly. It happened to me and i just couldn't figure out why i was having such a hard time on a hot hatch time trial, until one of our DC GAF regulars pointed it out. If it is indeed busted, you could remap throttle to another button, or get your DS4 replaced.
Alternatively, if you fall behind a ghost immediately after the start, it could also be that the ghost wasn't recorded on its first lap and crossed the starting line at a higher velocity than your starting speed, so it might be worth doing a couple of laps, trying to nail the final corner before the start/finish line, and see if that makes a difference. Usually it shouldn't make a huge difference though, so i'd check the R2 button first.
