Obtain A license for instance; from a fresh start? Or with all cars unlocked?

Ummm.... Firstly, in order to unlock all cars, you need to get Burnout License; which is above A license.

And secondly, for speedrunning in general, most categories for speedrunning would be New Game, or New Save File as default, unless stated otherwise (NG+).

So to answer your question, a new game.