Immediately toss your rifle, you won't need it and you'll run faster without it. Run all the way around the right side of the compound, around the back, and to the edge of the water near the bridge. Quickly dive into the water and swim across to the other side. Crawl up the embankment on the right side of the bridge and get your silenced pistol out. Here's the trick. You have to kill both the guards before one of them manages to hit the alarm button.
Without wasting precious time, shoot one guard in the head and quickly fire two round into the back of the other guard as he moves to the alarm button. If you've done it right, both guards will be dead without the alarm going off. If one of the guards does push the alarm, start over again. It'll take a few times before you get the hang of killing both guards that quickly.
Once you've killed both guards, fire a single shot into the camera right above the gate. Then, jump onto the rail of the bridge, run around the fence and over the bridge gate. Open it up and run as fast as you can diagonally to your LEFT and straight up the sloping hill. Keep following the fence until you come around the back entrance of the corner building. Don't stop running.
Run along the wall and stop at the very corner by the fence enclosing the generator switch. Lean around the corner and when the alarm turns away, run to the chain and pick the lock. Quickly turn on the generator and then get back out of there and get underneath the camera as fast as you can and over to the first switch. Hit the switch without stopping! If you do it right, the camera will only blink red a few moments but will go back to being green without sounding the alarm and you'll be past the view of the camera and standing by the second switch. Wait for the platform to reach ground level. Hit the second switch and jump in. Ride the platform down deep into the mines.
If you do this all perfectly, you can beat this mission without having been seen, 100% health, and under 6:30 minutes. My record time was 5:57.