Right here is a large portion of your problem. Piles of loose dirt. Then it just looks like they walked around on it and spread it out some. You never ever want to have loose soil under a slab. When i had my garage foundation put in, and when I had the wifes building's foundation put in....footers were dug, rebar laid, wrapped around the corners, and footer concrete poured. 2 days later they laid block.
In each case, the topsoil was scraped off including sod. You never want sod or turf under your slab.
Also in one pic, you show that there is a crack at the end of your control joint. That will happen as they can't get the saw up against the foundation. Almost everyone will do it, and mine did also. That is no big deal and can be filled. Also the slab cracking at the control joint all the way through, that will also happen and no huge deal, AS LONG AS THERE IS REBAR to keep one slab from dropping lower than the other slab. Wire won't keep one from dropping or cracking, rebar won't keep a slab from cracking, BUT it will keep on slab from dropping lower than the other. And fiberglass will not keep your slab from cracking. PROPER PREP IS THE ONLY WAY TO KEEP THINGS FROM HAPPENING.
I have a sidewalk that is maybe 70' long. I dug it down about a foot or so, then had gravel put down. The Bobcat had a 5' wide bucket, the sidewalk is 3'. I had the gravel down for a year before I poured the sidewalk. I rand rebar down through where the sidewalk was going, doubled up at where each control joint was going to be. It's been down, close to 12 or 13 years no and not one crack. I forgot to pin the sidewalk to the concrete at the garage, and it will raise up maybe an inch in certain parts of the winter with frost heave, but no cracks.
And I understand, that when you go to build a garage, it's not possible to have crushed stone down for a year before ever pouring a slab, but compaction is the key to having a flawless slab. I can go around my garage and thump the floor with a spud bar and tell you where every hollow spot is underneath due to settling. But the control joints have kept the slab from cracking where it shouldn't.
Good luck with your quest, and DO NOT let the contractor put you off until next week, then the next week. Because if you do, he'll drag his feet until October, then tell you that you're screwed. I have a buddy that is pretty damn sharp. He had a house built that was the house from hell. Everything went wrong. When he couldn't get any satisfaction from the contractor, he finally called the State's Attorney General. It ended up that the contractor had to buy the house back, and then some for the inconvenience caused.
But whatever you do, DO NOT let the contractor put you off, and do not let him cut corners to repair the problem.
If anything, other than tearing it completely down......tell him to put a proper foundation in behind the current foundation, slide the garage back after things are in proper, then repair the old foundation proper. You'll be setting back a little further, but would have a nice parking area in front of the new garage. And make sure things are compacted proper.