Hi, sounds like you have got an idea to use something like lasagne gardening to develop your beds.
You start with a layer of cardboard over the grass/weeds. You then add a layer of manure and alternate green and brown layers until you have about 6 layers of depth, then top with compost. You can then either leave the bed to rot down before planting or plant plug plants you have raised in the meantime. I have had good results (see my ecodolly diary on here for information). I am gradually surrounding my beds with wood, but this isn't essential.
This is what I have used to quickly convert my overgrown plots I took over (which were wall to wall couch with little else growing in them). Sadly, I haven't been able to use the concept for the last half of my second plot as the soil is full of plastic, carpet and other junk and it is all different levels. If you have a relatively level site, then it sounds like a good idea.
This was the half I tackled last summer (I took the plot over in June) and how it progressed. I managed to get excellent courgette, winter squash, celery, salads, cut flowers and chard crops out of these beds within a very short time frame - no digging required other than grubbing out a few large perennial dock plants that were growing.
To explain the pics: 1) taken when I took over plot, 2) After first beds set up, 3) planted up 4) end of season. The weed suppressing membrane was just the start of paths I introduced between the beds.
At the end of the summer, I planted cabbages, cauliflowers, garlic and onions into these beds having added a little pelleted chicken manure to the brassica beds first.
By the way, you don't need to set up beds - you can use the concept over a larger area if you wish and if you have the raw materials to do so - it is just that most people use beds with this method. I also have bark chip paths to reduce the maintenance as I find, with grass paths, I am always fighting the couch grass from creeping onto the beds.
There are lots of articles available online and youtube on lasagne gardening.