Hi, My version of no-till. lasagna, square-foot gardening is as follows. Last year I took cardboard boxes and laid them on my lawn and then covered them with mulch. Later I decided that the soil underneath was too acidic so I raised the cardboard in areas I wanted to plant and sprinkled lime and compost and re-layered. I did a garden before where I dumped compost, food scraps, bagged soil, bagged manure, and topped it all off with straw. In both methods, when I was ready to plant, I either made an opening in the top mulch layer and put a handful of "good" soil and planted in that, or I pulled back the mulch and made an opening through the cardboard and planted it directly in the ground. In areas I planted later, the grass was dead. In areas I planted earlier, I pulled the grass out being careful to mulch heavily around the plant.
As for starting with kitchen scrap plants, I have had good luck with pepper seeds, and the cuttings from onions. You can google and find dozens of "scraps" that will root.
Good luck - but beware -all big gardens start with 1 plant!