Are you using a fixed physics timestep? If not, that’s the first thing you need to do. The engine doesn’t support this, you have to add it. Semi-fixed and variable timesteps won’t give you accurate predictions (on any physics engine).
Your approach won’t work well because you’re mixing objects in different time streams. The vehicle is in the past, but everything else is at current time.
Better way to think about it is rewinding time and catching up (predicting) to the current time, rather than fast-forwarding. In order to accurately do that, you need to know the entire state of the world at that time in the past.