you could have the other cars movement component disabled then enable it when certain conditions are met, for example when your players velocity is greater than 0. show below is how this could work though this is just a test setup and i do not recommend using the exact setup. basic idea here is to have a timer or something that checks the players velocity then activates the opponents. this could also be done with a event called from the player or a interface call.
another method could be to disable all cars movement component then just activate them all at once so the player and the opponent can begin at the same time. you could easily inset this script right after the go is called.
note i tested with characters and not the vehicle template so things may work a bit differently.