The prep seems to be the main thing. You might be an excellent candidate for checking out a new groundcover/sod alternative called Kurapia. Its a spreading 1" high groundcover, that for your application, has the added benefit of a vast root structure that helps retain soil on hillsides. It's used a lot to stabilize drainage canals. It is drought tolerant, pretty, attracts pollinators with white flowers, is obviously 100x easier to install than artificial turf, and safe for your kid. Just a thought.