You can rise above just about any soil problem by building a raised bed on it and filling it with good soil. People have had vegetable gardens on unused driveways in raised beds.
Beds can be made of anything that holds in soil. In fact, if you slope the sides of the bed at about 45 degrees, it will stay in place with no wall at all—just a pile of soil. Functional beds can be made of concrete blocks without mortar, boards nailed to stakes, stones from the field, old bricks, or railroad ties.
The beds can be from 6 inches to any depth you want. Grass and annuals will grow in 6 inches of soil—but keep them well watered; that little soil dries out quickly. Most vegetables or perennials need 8 to 12 inches of soil. Shrubs and trees need 2 to 4 feet of soil.
This method of growing can be used to reclaim poor soil. If the bed is taken apart at the end of the growing season and the soil dug into the native soil, the ground will be improved and perhaps able to support a garden the next year.
In Israel, a similar technique was used to reclaim desert as farm land. Bales of straw were laid out in rows and a few inches of soil placed on top of them. Seeds were planted in the soil and were watered and fertilized through a drip irrigation system. The straw rotted fast enough to support plant growth as the seeds grew. After harvesting the crops, the straw was plowed into the field.