Congrats on your first chin!
First thing, are the mats very big? If they're small, I would be inclined to leave them until she gets a bit more trusting of you. Of course if they appear to be painful, then I would remove them. But you'll have to grab her, hold her by the base of the tail and attempt to comb them out, by combing from tail to head (opposite of how you'd do a dog) with a flea comb. Otherwise you can try to rub it between your fingers and see if it comes out. Lastly you can try some baby wipes and try to work the mat out if it isn't too huge.
As far as getting her to trust you, it will take some time. I'm not sure how new she is to you, but for some chins it can take a month or more until they really trust you. What I would do is go by her cage every day and just talk to her. Don't stick your hands in yet and just talk. Then you can work up from there by putting healthy treats like old fashioned oats, an apple twig, a small shreddie, a cherrio, rosehips etc. into your hand and just putting your hand in there and letting her come up to you and get them out of your hand. Once she's comfortable doing that, take her to a chin safe room (like the bathroom) and let her run around on you. If the cage is small enough, take the whole cage into the bathroom, so that you don't have to worry about catching her to put her back in.
Just take it slow. Don't let her out to run around until she's used to you, because if you spend time chasing her to try and get her back into the cage, you'll only be taking a step backwards.
Some chins are friendlier than others, and some will never like to be held. They aren't like cats or dogs and many actually prefer not to be handled. Only 2 out of my 4 actually don't mind being held.
Good luck and feel free to ask more questions
