Amazing that there are comments on here suggesting you go from flipping burgers one day to driving a tow/push back tractor the next. That's a bit like suggesting the next time an aeroplane crashes that the pilot was flying a drone one day and Captain of a wide body the next!
The GHA have a hierarchy on ramp jobs and driving a push back tug is only for experienced staff because oddly enough the GHA know it is a job that requires experience and competence.
The last GHA I was with had a 3D simulator that push back drivers had to master before being licensed to drive a push back tractor. This was configured with 4 different backgrounds of stands at the airport, including the 2 that were considered more challenging. On completion of their training they were licensed initially for narrow body aircraft, and only when assessed by the trainers as competent did they move on to additional training for wide body aircraft. Your airline will also have sent your auditors to check the training of your GHA, and push back training and licensing is always covered.
The drivers also have recurrent training every two years.
The other issue is that whilst the centreline is there as a guide, it isn't necessarily relevant to all aircraft types cleared to use the stand. Sometimes there will be a dotted line to follow for certain types that required a wider turning circle, but that is down to the airport operator to arrange.