Avid backyard gardener here. When we moved to our new house in Fort Wayne our yard was a real problem child. It was a new build in an old neighborhood. All the other houses where about 40ish years old. Ours had also had a 40 year old house, but at some point that house was abandoned, eventually condemned and then knocked down. Eventually a builder snapped up the lot and built our current house. But that means the ground had been stripped of topsoil and compacted all to hell not once, but 3 times in the past 40 years. What was left was dead heavily compacted clay subsoil. It had drainage issues in wet weather, it developed crazy deep & wide cracks in dry weather, and just generally didn't want to grow anything.
We solved it by dumping around 400 cubic yards of arborist woodchips spread 12-18 inches thick over most of the yard, then top dressed that with composted manure and worm castings. Finally, we planted a bunch of wine cap mushroom spawn (to break down the wood) and clover (to fix nitrogen and feed the fungi) over the whole thing. 3 years later we have rich loamy soil that drains well, is full of earth worms and grows anything we plant it it.
TL;DR: Add tons of carbon and nitrogen into degraded soil and the local fungi, bacteria and worms will turn that into good soil if given sufficient time.
It's not a hard transition between the layer I added up top and the stuff below, so bioturbation is happening - but it's a slow process. I've helped it along a little with broad forking but it will take many more years to impact soil 3 feet below the surface. On the bright side, that matters to me not at all, because nothing I'm growing has a root zone that deep. 12-18 inches of improvement is plenty for gardening and overkill if you just want a lawn.
Keep in mind pure organic matter does not a soil make. It's the mix of that organic matter + the inorganic substrate. So I added a bunch of organic matter to turn the dead compacted inorganic substrate (degraded pewamo urban complex series clay subsoil in my case) into good soil. The organic matter + fungi help that heavy clay to stable macro aggregates which let the soil drain. The humus the organic matter turns into help regulate soil moisture in dry conditions and provides the right environment for all the soil microfauna need to do their thing. Essentially I restored the O & A horizons, and over time the B horizon will improve.
Cover cropping is great btw, but you might want to get a soil sample analyzed. We had less than half a percent of organic matter when we moved in. Really you want that up in the 5-8% territory. More towards the higher end if your soil is clay dominant like ours. Cover cropping alone wouldn't have gotten us to that number in my lifetime.
I did get a soil test, but not for organic matter; I assume it's zero. My desert neighborhood has caliche under rocky sandy loam, but it also has a lot of very large old trees, so I'm hoping the caliche is permeable and not just that the original builders excavated huge holes. It's so rocky that a soil probe and broadfork is unusable, but as deep as I've tested (2 feet down) I've been able to still dig with a shovel.
This year, since I just moved in, I'm just doing a small 10x10ft testbed. I mixed in a few inches of compost manure, shallowly because the soil is so rocky. My plan is to do a biomass/nitrogen crop mix this spring, which is currently seeded, and then in fall do another similar mix along with deep rooted radish for decompaction. Then hopefully next spring I can plant real things. If I find that after a year of cover cropping the soil is still unusable, then I'll bring out the power tiller and pickaxe for the rest of the yard and get the amendments mixed in deeply. I've read a lot of permaculture books in the last year, and I'd like to garden in that way, but I'm certainly not against buying bulk amendments to get started.
12-18 isn't deep enough for me, since I am going to have large shrubs (need 3ft) and perhaps trees (need 5ft).
We are fighting entirely different battles. The main reason I'm focused on those 12-18 inches is drainage. Heavy clay will stay waterlogged for a really long time and basically drown plants. Once it gets really dry it goes hydrophobic and cracks. But down below the first foot or so, roots aren't breathing, they are just collecting nutrients - which clay tends to have in abundance.
If you are dealing mostly with sandy/rocky soil you've got drainage in abundance. It's possible you have a perched water table with the caliche - but if it's 2 feet of permeable substrate in a desert environment I don't think you are going to be dealing with enough water for it to matter, you'll just get lateral drainage. What you need a way to slow down infiltration, and also stop leaching since the cation exchange capacity of sand is hot garbage. Shade + organic matter is probably going to be your go-to tools. Unfortunately I don't think the free arborist chips solution I did will work for you - might be too arid for them to break down in a reasonable time frame. So it's either import it at cost, or plant and wait. Just boils down to your level of patience vs stomach for paying for "dirt" as it turns out good soil isn't actually "dirt cheap".
Something to consider - most of the no-till / permaculture folks admit that a one time tillage up front isn't that bad. The main issue with tillage is you are disrupting an ecosystem. The fungal networks, the worms, all the little critter infiltration tunnels. But that only matters when you aren't dealing with dead compact degraded soil. Right now there is nothing to disrupt, so if you can combine a one time deep tillage of organic matter, or maybe subsoiling to break up some of the caliche to whatever depth you want - now is the time to do it.
Yeah I'm totally fine with tilling at first, I was just trying to save money on renting a tiller.
Despite being sandy loam the drainage is really bad just a few inches down. I think the rocks are so densely packed together and in such great quantities that it's long to drain. I'm hoping the roots can get through and help this. If not, I'm going to have to rent a big tiller. One thing I've been doing that has obvious benefits is putting wet cardboard as mulch; the soil under the cardboard stays moist far longer. Unsightly, but definitely improving germination. I'll probably do this throughout the garden underneath landscaping rock since cardboard is essentially free.
We solved it by dumping around 400 cubic yards of arborist woodchips spread 12-18 inches thick over most of the yard, then top dressed that with composted manure and worm castings. Finally, we planted a bunch of wine cap mushroom spawn (to break down the wood) and clover (to fix nitrogen and feed the fungi) over the whole thing. 3 years later we have rich loamy soil that drains well, is full of earth worms and grows anything we plant it it.
TL;DR: Add tons of carbon and nitrogen into degraded soil and the local fungi, bacteria and worms will turn that into good soil if given sufficient time.