In Korea, children often start training as young as age three.
But in most western countries, the majority of children lack the focus to properly absorb Taekwondo techniques at that age - in part, because we don't permit teachers to harshly discipline young children. My recommendation, based on two decades of experience, is to start a child no sooner than age five; though if the child has a particular interest in learning the art (such as an older sibling who's been studying it for some time) that could be shaded down to age four.
The ideal time to start might be around age seven or eight: the student is old enough to pay attention and absorb more complex skills (such as entire poomse forms, or specific sparring combinations), yet young enough to be at their most flexible and fearless.
Although, in some in the U.S.A. you can start at 2 years old.