Most grasses will die if sufficiently shaded, but I’d consider what you want to replace it with in determining how to deprive the plant you don’t want from getting light. You could deep sheet
mulch , 3ft deep or more to really knock it out, or 12” and be ready to pull any sprouts. Or, solarize (wouldn’t be my preferred option, as it kills soil fungus). However, I believe that almost any plant is better than bare soil unless you have seeds, starts or saplings to put there instead at that moment. Grass is holding the soil, reducing
runoff, and building organic matter as it puts
carbon in the soil with sugars that are traded with other plants through soil microbes. Every time you mow and leave the clippings you are essentially chopping and dropping, not only adding the 10% nitrogen tops of the plant, but also the roots die back proportionately and in doing so effectively inject
compost. Ideally, I’d get rid of grass like natural forest succession does, grow other plants, especially woody perennials and
trees, The shade combined with fungally dominated soil life will suppress the grasses.