I believe that the possibility to push-start a modern car with a completely dead battery is a myth. I tried it once with a manual transmission car along with several workmates that helped to push the car. Even despite achieving significant speed, no gear would start the car. I even tried to turn the key at the same time I released the clutch pedal, just in case the car was designed not to be push started!
The problem is that typically, if the battery has no charge, it is close to zero volts. How do you excite the alternator's coils if the battery has close to zero volts? The alternator in modern cars is electrically excited and has no permanent magnets.
I ended up fetching my jumper cords, which helped to start the car.
If push-starting is practically impossible with manual cars, no amount of pushing will start an automatic transmission car. Of course, all of this applies only if the battery is completely out of charge. If there is some charge left, but not just enough to start the engine, the charge may be enough to excite the alternator's coils and therefore start the engine.