Grass will grow everywhere just some is particular where it grows.
Is this area shaded or in full sun?
St. Augustine requires full or part sun. Brumuda needs full sun. Zosia, can do OK in Shade.
I would tear up the soil. Rake it down to about 2 inches. Add some nice humus or shredded material. Rake this in so the soil is not as hard.
Spread down some seed or use sod strips. Don't fertilize the newly planted or seeded grass. Water every day or keep the top soil moist.
These grasses only should be planted around the months when the night temp is around 70 degrees.
Now, you might be able to get Winter Grass to come up, but it might be too late for that.
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