A breeder who is a groomer and runs her own pet lodge attended a meeting recently of the local golden breed club and this issue came up and she was asked for her advice--apparently she comes across this pretty often grooming dogs. If someone isn't showing their dog, she said the quickest, easiest way is to use grooming clippers (they are like an electric razor, but for dogs).
Mats under or behind the ears are best cut out IMHO. Usually if you do it carefully you do not even notice any hair is gone. I frequently clip behind the ears on dogs as a matter of course. Then make sure you brush behind the ears every few days to prevent the mats.
ETA: be very careful when clipping ear mats. We have had many people cutting their dog's ears while trying to cut out mats. Clippers are safer.
It's super important to brush your dog often so things like this do not happen. I brush Max every day and make sure I get his ears and armpit areas really good as this is where I've seen hair start to tangle. I let it go a couple of days and had some starting so this is something I learned through experience. I hope you got the mat out. You could try playing with it using your fingers and see if you can get it to loosen up / pull out. I do this with my long haired cat and it works - just takes some time. He likes the attention and I feel much safer than trying to cut anything out.
When trimming dogs and their mats, remember, their hair comes with the tangle when you pull away from the skin unlike humans...
When I cut mats out I always place my fingers against the skin so I won't cut him....
If you have to cut, slide one side of the scissors along the skin between the mat and the skin, and then cut into the mat in the direction of the hair growth, so you cut the mat into half (or smaller segments) and then you can usually work them out easier. That also helps prevent too much of a hole. Having some thinning shears on hand to thin out the hair behind the ears helps prevent them too, and if need be you can cut the hair above the matt with them and then work them out as well. Just be careful (if you can put a comb in the hair then cut on the side of the comb you won't get skin).
A product I've used (similar to hair conditioner) is Cowboy Magic that you can get at a Tack shop (where products for horses are sold). This product is amazing! Kind of like a thin/watery ointment that you massage into the mat. But, hair conditioner would probably work as well.