Soil preparation question

I have been slowly turning my former lawn/landscaped back yard into plots for planting mixed vegetables. A lot of this area is super compacted clay with little to no life as it’s been underneath a weed mat.

I’m generally planning to do no-tilling, but for this initial start I have been digging down around 2 feet and mixing the native soil with mulch (smallish woodchips and sawdust from a tree I cut down) before I then add a top layer of mulch. I plan to add cow manure to the top in the early spring before planting next year.

My question is, is this going to help or should I just be applying the mulch topically and not digging down? Not sure how to break up the clay best and get the microbes back.