Understanding whether soil is truly "compact", is made made more difficult because tillage, to break up soil, is so general.
Gardeners and farmers have been led to believe that soil needs to be loose for seeds and plants to establish. Yet this is untrue. Roots love firm soil.
Steph and I are asked a lot about "compact soil" and the answer depends on whether your soil is really and truly compact, or firm.
Compact soil is dense, smelly (sulphur!), sometimes grey and rusty orange in colour. Fortunately this is a relatively rare occurrence, usually caused by heavy machines, in wet conditions. Or by excessive cultivation which knocks out all natural soil structure, and kills soil life.
Firm soil is normal and good. Soil is hard in dry weather, but there is a matrix of structure from not being cultivated. I am currently planting into hard soil, but with a soft surface of compost.
Incidentally you can walk on no dig beds! The structure created by soil life is firm and stable.
Maintaining a surface mulch of organic matter is the pathway to open, aerated yet firm soil. Don't worry if you soil feels hard. As long as you feed the soil life, from above in nature's way, your plants will grow.