I wouldn't recommend waiting for the artillery unit to blow up. Start running towards the upper edge of the map. You'll have to reach the extraction zone. Thankfully, there's only one path leading to your destination (#1). It's very important that you don't stop because a lot of enemy units have appeared in the area. They will be chasing you (#2). Avoid most of these attacks. Keep moving towards your target.
If you've started this run early, you should be fine. The extraction zone is just around the corner (#1). There's a UAV parked there. You will have to get close to it. Press the X key in order to take a seat inside (#2). Now you will only have to wait for the mission to end itself.