Funny, I recently bought a place and I'm planting a garden. The soil is so clay heavy I could throw it on a wheel, and fire it to at least earthenware temperatures. This also means a rototiller is useless, so I've been using a shovel to remove the grass layer, which I pile up around the edges of the bed, a fork to break up the top 10 inches of clay, and then a wheelbarrow and shovel to cart over topsoil from a pile I had delivered. In a post-apocolypse world, we can omit the delivered dirt, because you wouldn't choose such crappy soil to start with.
I'm 45, not a weightlifter, runner ... not even a regular exerciser. I'm a little chubby from sitting at a desk all the time. In about about an hour and half I can dig up, till with a fork, and wheel barrow over a 10" layer of top soil to do a 10x10 area. This gives me about 20" of planting bed, the 10" I broke up with a fork and the 10" I dumped on top, the grass clumps act like the frame for a raised bed. If this was done in good dirt without the need for added topsoil, subtract half an hour because of easy digging and no dirt hauling.
If I did two of those beds per day, one in the morning and one in the evening, I could dig up 1400 sq ft in a week.
It looks like I'd need about 23,000 square feet to feed myself, but some of that can be made up with space devoted to animals -- most though still goes to garden.
I started this post feeling sort of positive, but tilling soil in this manner burns 4-500 calories per hour. Do this for three hours per day on a 2000 calorie/day diet, and you're going to turn into a rail fast. If it was only 400 calories to dig 100 sq ft of easy soil, and I had to dig 15000 sq ft, I'm going to need an extra 60,000 calories to make it -- an extra month's worth of food to invest in labor to plant a garden. It is sounding increasingly unrealistic to hand dig a garden in the absence of outside inputs, i.e., food for the digger.