If you are pushing the car on a public road it means you have already failed at driving safely.
Driving safely != not cause an accident
Driving safely == not be in an accident
You can be the best driver in the world driving the best car in the world and it doesn't matter, because some idiot will not look in their mirror when changing lanes and suddenly you are in an accident.
To drive safely on a public road means to take care for your abilities and your car but most, most importantly, too give wide berth to other road users and to drive in a way that will minimize the accident if it happens.
Understand everybody makes mistakes. If you aim to drive safely you need to make it your responsibility to drive in a way that will allow yourself and others make mistakes and still not cause an accident. In other words, give margin for error.
Some examples:
-- try to minimize your time in somebody's blind spot.
-- observe traffic behind you, not just in front of you. I have on multiple occasions avoided a car hitting me from behind, twice at a difference of speed that looked like at least 100km/h. Being aware where the cars are gives you ability to act instinctively without hitting somebody.
-- try to maintain slow relative speeds with regards to other road users. For example, never drive fast around cars stuck in traffic.
-- always have a backup plan for every maneuver. For example, do not have fast closing speed to the car in front of you with a plan to change the lane just before you hit it. You need to maintain the ability to break in case the car in front of you suddenly slows down or in case you can't change the lane for whatever reason,
etc.