1. Where do you live
2. what are you growing
Personally, I would till the ground it was going on top of - if you dont have a tiller - do it by hand(4 x4 areas is probably too small to till anyways) - you need to just break the soil up - if it is currently grass - just turn the grass over and chop it up with the shovel - no need to remove it. Break the dirt up good either way. The roots of most plants are going well beyond 7inches down. Tomatoes can go several feet down.
Personally- I would just fill it with top soil or - if you know someone with a farm - good composted soil. Fill it right to the top - water it to settle it - and it should be a little below the top of the bed so water doesnt just run off.
Thats it - I think you are way over thinking it. Again - depending on what you are growing. But most vegetables will grow quite fine in plain old top soil.
My mom can grow anything - she puts a stick in the ground and next year she has a bush - she's amazing. She says never use fertilizer - it is like crack for baby plants and they will get dependent on it. I have always followed her advice on that.
Then in the fall - load it with leaves or other organic stuff - turn the dirt and let it get nice and composted for next year.
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