It depends on the person, and their interest and willingness to practice, and if they have a talent. Mozart, I believe may have been about 5 yrs.old.
if a child is gifted, sometimes it can be recognized at an early age. I didn't even know what a violin was til 10th grade, then I learned quicky and got a scholarship to major in it in college. but that is sort of a late time to start.
In college, they tell us to offer it in public schools beginning at 5th grade. But private lessons depending on the method can be started a lot earlier.
Just make sure if you start a child at any age, they have an instrument that is appropriate for their size. If you ever bought shoes a little big to allow for growing room, you don't want to do this with a violin. because if they cannot reach where the fingers need to reach, then they cannot learn well, and will be hindered and discouraged.
One of the most important issues is whether the child will be willing to practice and keep it up. Not just try a lesson and quit. If it is just a passing thing, like so many americans are with a new toy, a violin is expensive to purchase, and then they treat it like a toy and throw it in the corner when something else comes along.
violin is a nice instrument for boys and girls.
viola is nice, but a little larger and heaver.
Cello has a nice mellow sound, my son preferred it over the violin, because he said it had a nicer sound and the violin had a squeakier sound.
the instrument has a lot to do with the sound. The violin he started with was a cheap one that had been passed around and didn't have a proper size bridge when we first got it. It was a discouragement for a beginner . The instrument makes a difference on whether the child will like the instrument or want to go on to something else.
Hope this helps.