Thanks for the pictures, which help to clarify what you've got there. Not a lot of grass, by the look of things, which isn't surprising given the lack of sunlight under the magnolia - but plenty of little weeds, which include a lot of violets, and moss. I can see a couple of smallish dandelions near the tree's trunk but I doubt if there are many other "problem" weeds there.
You might get away with laying THICK mulch over there without killing the weeds first, but it'll need to be thick enough to exclude light or they'll carry on growing. And you'll need to get rid if the dandelions cos they grow through anything...
At the edge of the area where there's concrete edging, I think you might have difficulty getting the mulch thick enough, without removing grass/weeds first.
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