You do see them, but you don't notice.
Their beaks are slightly flatter and wider than an adult's and for the first week or two after leaving the nest, the feathers around the base of the beak are bristly and lay back along the face. You may occasionally see one begging a parent to feed it - it will normally run after the parent, quivering its wings and sqeaking - hence the name for a very young pigeon, just feathered - a squeaker.
During their first week of life baby pigeons are fed a high-fat, high-protein diet of crop milk produced by both parents. They grow very fast.
In the case of domestic/feral pigeons, they walk well at about 18 days of age and start exercising their wings about a week later. But because they have been regularly fed by the adults and haven't done much exercising, the babies are often bigger than their parents by the time they start to fly, which is on average 30 to 32 days after hatching.
Many other species of pigeons will rear their young to independance in under 3 weeks.