Without seeing your soil I cannot be certain but as long as at least some organic matter has been applied during the past year, there should be sufficient life in the soil, worms and beetles moving around, even slugs, also fungi threading along etc, to provide sufficient passages for developing roots.
There is a major difference between compacted soil and firm soil, I suspect you have the latter which is great, and as those roots of old vegetables rot away, they will leave both organic matter and air passages, which new roots can then fill. I was extricating some carrots this week (Purple Haze and Early Nantes) whose roots are long,and the bottom three inches was covered in dense clay when I eased them out, really dense looking clay, but obviously they are rooting through it very well. Because the soil is so moist at present I did not even need a trowel to loosen the soil at all but in dry weather I do need to as the clay becomes even firmer. But everything grows fine! Incidentally the carrots were sown in compost applied to the surface, germinated strongly in it then rooted into the undisturbed clay below.
Many people believe that roots can only travel in fluffy, recently loosened soil; my experience suggest otherwise. Let us know how it goes!