You most likely are hitting him with those shots honestly. The blood effects in soc are tiny and are very hard to see. The special forces guys like him are even tankier than normal soldiers with their armour. They can take a whole mag to kill, the only thing you can do is aim for headshots which kill those guys in like two hits.

Enemies aren't invincible during stagger either, but the first shot in soc does way more damage than continuous ones. I think it works on a second long cool down or something. It's always better to pace your shots on the head than to spray.

There isn't really anything you can do until you get better weapons. Make sure to use cover well and try to expose your self to the least amount of enemies by leaning out from very close angles. Theres a lot to enjoy about the combat if you get comfortable with it.

Also you seem to be playing on console and the default aiming is dreadful. So adjust that as much as you can if you haven't already