Some things happen more quickly than others. I don't really have a plan, except a vague one, to get rid of all mowed areas that aren't walkways or the dog's part of the yard. Too much wasted time & money on mowing all that which isn't pretty or edible. I got rid of the white thing in the above pic & put cardboard instead ('cuz I happened upon some great sheets of it!) As I dig up grass, I'm putting the chunks here in the back. Next spring, it should be ready to use, full of "good dirt."
I keep digging it up from the front, as I have the gumption (and plants to put there.)