How do you get grass to grow in a yard that won't even grow a weed

I would take a sample of the soil into the county extension office and have it analyzed. That could tell you a lot.

Try ground cover. Put down some mulch then just throw some chunks of it on the mulch. Go back through and put a handful of mulch on the roots. My grandparents couldn't get grass to grow on their property, or weeds. I did this a few years ago and it's all filled out now. Looks a lot better than bare dirt with minimal care. Drought friendly too!

We looked into this and got the liquid lawn that is sprayed on like foam with seeds and it takes root in the foam. We just watered the lawn to keep the seeds growing until they got established. We plan to do our backyard next. It is called Hydro Mousse Liquid Lawn and you can order from Amazon or from the lawn company directly at www.HydroMousse.com

You need to make the soil healthier! Half of my yard used to be same as yours but then I applied a few easy strategies, like adding organic matter such as compost, shredded leaves, grass clippings etc. and adding more soil amendments. This article gives great suggestions on preparing soil for grass seed https://theseamanmom.com/how-to-prepare-soil-for-grass-seed/

If weeds won't even grow there... consider that someone may have treated the weed with a total kill preparation... you will need to dig up some of the soil... and put it in a pot... plant Pansies, geraniums or marigolds in the pot... and see what happens... if they die right away... and you have cared for them properly.... then you might need to replace all of the soil in that area of your yard.