So you're talking about a vegetable garden in the new space? I till down about 6 inches in order to mix in compost, lave sand, green sand and molasses into the native soil. After that, I do not till again in order to allow worms and microbes to settle in and do their thing.

Usually what I do is remove all of the sod before you till. Then I put the framing on top of the bare soil, add my compost and ammedments and till all that in about 6 inches. Plant and mulch heavily. Since I have either heavy clay or white rock in my soil, I usually have raised beds. Not much of a weed or grass problem.

You put that over your grass?