Remember that Garrett isn’t a fighter. The games have been a little inconsistent on this point, but the character your looking at is one who survives on staying out of sight, avoiding detection, and only removing guards when there is no other possible option. In a straight up fight, he will lose. It’s just not his skill set.
Ironically, if you’ve been playing the games, you should have a pretty good idea how to follow his approach to hostile environments. As with everything else, it varies between the games, but Garrett’s best approach to danger is slipping away undetected.
If he’s being chased, his best option is to find a way to disappear. Although it’s not a very Thief concept, blending into a crowd and slipping away is one of the best immediate responses. Failing that, finding ways to take a path his pursuers don’t see, or can’t take is the other solution. Garrett caries a lot of specialized tools, including things like the flash mine to deal with pursuers. Whether he uses the resulting confusing to blackjack everyone who was stunned, or escapes is up to you. These kinds of gadgets are, somewhat, a staple of this archetype, so it’s not an unreasonable suggestion.