Driving emissions numbers I remember off the top of my head are Swedish averages, around 2.5 tonnes CO2e per year (15000 km/year). This is averages for the Swedish car fleet, which tend to be smaller models and more modern than many countries.
So: sure, production emissions are a big factor, but driving the car can easily win the efficiency savings back in a fraction of the car’s lifetime.
On the other hand I also know people who drive a multiple of that.