Yes that is more simple. If you push something, it moves.
If you push your own car, it moves but you are outside of your car when you push it, with your feet on the ground , using your legs as the energy source.
For your working rocket, you are asking me to believe that I can get into my car , shut the door and push it from inside.
Basically you are telling me that the rocket pushes against itself.
Well, is not the rocket actually pushing against itself, its the gasses at high pressure (expanding a lot faster than if they were just released into vacuum) pushing against the rocket.
I can't make a comparison of it with a man pushing a car, because the gasses are constantly leaving the rocket. So it would be like the man just pushed the car once and stayed outside, but that would be just one explosion, it would be more like a bus full of men, one jumps out of the back window and pushes it, then the next does, but they are pushing using friction against the floor to move the bus more efficiently, in the rocket, the explosion is gas expanding, only pushing against the rocket, so it would be more like each man jumping in the air and kicking the bus, the men are the fuel, the bus is the rocket and the kick is the explosion. Of course that is not at all an effective way of moving a bus, just trying to make a comparison of what would it really be like if we wanted to transfer this to men and car, this explosions generate a lot of energy, enough to move the rocket.