Can I only claim vehicles that I have driven for self-employment?

When I first started my job as an independent contractor in July 2018, I initially started out with my manager driving me around in her car for training. As training progressed, I started becoming more independent and driving to some of these places in my own vehicle. I just want to confirm that I would not be able to claim the mileage from my manager's vehicle because I was not initial operator of that vehicle.