There is more than one way to skin a cat.
Change your way of visualizing a garden to include containers, raised beds, large areas heavily mulched with clipping, trellis', and whatever else you can imagine. We don't have to have the garden Grandpa had. I can't have Grandpa's garden. First off, the tractor he bought was more economical in his day and was made better to last. Then Grandpa had more land to work with than me.
Today we know about mulch and raised beds and so many other things.
I have blackjack for soil. Imagine sectioning off a 'garden' and putting as much clippings or pine needles as you can conceive of, then decide where your 'rows' are. Now every foot or so, where you want a plant, you disturb the soil a little and add about 3 cups of improved soil to get the seed or plant started good. Now put the mulch back. Do the whole garden like this and step back. Notice that most of the garden isn't really planted, but is mulched. All that mulch will decompose and will improve your soil. Be patient.
Keep a compost heap. I used to put all my table scraps in mine, but then cats started eating most of it. I used to look at them and say, if I only had chickens again, all that food would be turning into meat and eggs.........done. I also put coffee grounds in the compost. And now I put chicken droppings in the heap a few times a year when I clean up the roost. I just put weeds or pine/cypress needles under the roost to catch the droppings. Great compost. You do this and you always have improved soil to use in small spots. A lot of stuff that ends up in people's garbage, could be used to improve your soil or feed animals (which is compost, only super fast).
Raised beds might cost you some $ to get started. I guess it depends on how you set it up. I have some that were done free by just accepting some tractor tires that were too worn. I know some people are afraid of them because possible leaching problems, but it hasn't killed me yet. But the retaining wall blocks have costed me a lot. DH and I wanted raised beds due to getting ready for old age and for living in flood zones....plus you can grow a lot if you use square foot with the absolute best soil.
A couple of years ago, DH had a stroke of genius. He cut bottoms out of some black plastic planters we had a stockpile of from years of buying trees and plants. He dug small holes and partially buried the bottoms of the pots and filled the bottom with the missing soil and topped it off with good soil and inserted cucs, tomatoes, bells, egg plants, squash (actually we didn't do so good with the squash). We did pretty good and he just cut grass around each plant, except for the plants that needed trellis'. Those got a quick trellis set up in about an hour. He even managed to make it look nice. I was actually proud of him.....well, more than normal. It did bring some food in the house.
Now before someone patented the term Lazagna Gardening, I had the good sense to know that cardboard would rot, in time and in the meantime, would keep the weeds at bay. So imagine if you have a large area you want to work with and have a limited amount of clippings, leaves and needles to mulch with. Save all the cardboard you can, to use to mat down the ground and use the mulch material sparingly. You can add more over the cardboard, if you have enough once you finish the job.
I haven't had a tiller in about 14 years. A relative was suffering from dementia and forgot I bought his tiller. He pulled it apart in his shed to 'fix it.' I told everyone to leave him alone because as long as he was messing with the tiller, he wasn't busting the house apart; and besides he was happy. So I've had to do some smart gardening, instead of all those traditional rows. I can't say, I've not needed to buy some produce here and there, but I assure you, we've taken care of most of our produce needs. It can be done. Just come up with a plan and carry it out.