Quite frankly I think the image is a bad fit for the task, presumably the photographer was not aware of how the image is now being used and the noise is pretty bad to boot (though the jpg artefacts may be a factor, too).
Do you have access to the RAW image? If so developping it in 16bit and with more attention on the noise might provide a better starting point.
I think Select > Subject does not do a terrible job but much of the fine hair gets lost.
So one can try to isolate the areas of the most meaningful separation of forground and background in the channels and try to combine them; but ultimately I doubt that a lot of manual input (aka painting) can be avoided.
You need good contrast between the Hair and the background for a good extraction. Your image is quite dark lacks contrast and I'm colorblind so I do not do color well. Still IMO select subject did an acceptable job given this difficult image. You are not going to be able to extract her stray hairs.