Is it ok to drive car immediately after starting the engine?

I doubt that it would be possible to get the thing into gear and take off before the oil pressure comes up. I think they just want you to wait for the lights, airbag diagnostic checks, etc…to clear before you go. Start it up, get your seatbelt on, and go. There is no need to warm the engine up unless it is extremely cold, and then you might want to give 30 sec. or a minute.