Raising the soil level surrounding the base of an established tree is pretty much a recipe for disaster!! It serves to smother the root system and can lead eventually to the death of the tree. And planting in the existing conditions is extremely problematic with most maples - they have an aggressive and surface-oriented root system that pretty much sucks out any soil moisture and nutrients, making it difficult to impossible to establish any underplantings.

The best you can do - both for the appearance and the health of the tree - is just to make a large mulched area surrounding the base where the grass no longer grows and covering the exposed roots. Just a couple of inches of wood chips, pine straw or chunky bark. This will allow proper oxygenation and water penetration and tidy things up without harming the tree. Just keep the mulch several inches away from the trunk to avoid moisture accumulation and prevent rots.

I fully agree with gardengal's response, in its entirety.

In terms of plant suggestions, I've seen mondo grass that volunteered flush against the trunk of a large silver maple, where the ground is more root than soil. Many bulbs do great under this maple, including iris reticulata. The roots seem to deter bulb eating rodents. Evidently cyclamen coum and hederifolium do well with maples. The soil is dust dry during summer.

I've thought about trying a ceanothus near there also. Maybe a boxwood or abelia if you put it in fresh, root free dirt (away from tree) and in some shade and water it to get it going, though this might just attract the roots to invade faster! I've seen boxwoods that volunteered and were growing (slowly) in very dry shady summer locations also.

Fyi, some think groundcovers should not be planted under trees as they steal nutrients from the topsoil and starve / stress trees under which they are planted.

....and maybe someone more knowledgeable will comment on whether those are girdling roots on the maple in your photo.

It looks like you might have some sun. I like to plant daylillies under my part shade shrubs and trees.

We used to live in a house with a Maple in the front yard. The space was fairly small and got full western sun and some from the south. Up against the house was a raised flower bed - of course full of tree roots and shady in the summer. What grew well in there was those large old tulips - in yellow and red - which someone had planted deep. The only other thing that I found that would work there was primula or primroses. Primula loves sun in the early spring (before the leaves came out on the maple) and shade from the heat in the summer. The tree was about 10+ feet from the flower bed and we are in zone 5b or 6.