Yeah that part is a pain in the aass. Unfortunately, i deleted ùy saves because they were taking like 3 Gb, I have some advice though.
After you get pst the drunk guy who calls you blondie and the first guard, wait for the first patrol wave to pass, then you need to sneak at the left, behind the tents, when you see the cook, don't be afraid, go to him and convince him \/ to go to sleep, then trigger the second wave of patrol out from the gate, and go hide till they leave, after what you go through the gate, and there you go, you are out.