You are in the army no and you need to do your part, so the soldier can win the war. Everything is crucial, even if you aren't fighting the front line, you are still a valuable part of the army. You don't need to risk your life all the time as there are roles that need to be done. Like the medics, you too have an important role as you are the truck driver and it is your job to deliver the supplies to the front line. They would be counting you for those supplies.
Wait for the supplies to be loaded at the back of your truck. Drive the truck when you see the green lights as that indicate that you are cleared to go. Drive with safety in mind since you might not get to your destination if you can't do that. You don't need all the cargoes, but it would help in your scoring if you can deliver more than enough cargoes. You can see the required cargoes on the upper right portion of the screen. You can't pick up those supplies once you lose them on the road, so be extra careful. The game gets harder and harder as you make some progress.