Two different things get bundled into this question, and they start at very different times.
The two
| Starts working at | Why | |
|---|---|---|
| Saying out loud what they just did | As soon as they have words | Needs no counting, no memory, no waiting |
| A total that adds up | Around four, properly by five or six | Needs holding a number and a future at the same time |
The part worth starting early
The naming. It costs nothing, it needs no equipment, and it is the half that does the actual work at every age afterward. A two-year-old who hears "you gave that back" is learning the same thing a nine-year-old learns from it, just without the arithmetic attached.
The part worth waiting for
The chart. Starting it too early usually means an adult maintaining a system a child is not participating in, which quietly becomes a chore and then stops. There is no cost to waiting a year and there is a real cost to a first attempt that failed, because the second attempt starts against a memory of the first.
The upper end
Charts stop suiting most children somewhere around twelve, and what replaces them is the same idea in adult clothes: agreed things, agreed values, and nothing that can be taken back. The mechanism does not change. The packaging has to.