There is no specific age at which to begin playing the violin. Some musicians will pick up the instrument as early as the age of three, while others wait until retirement to find a new hobby.
Anyone who has the desire to learn, should be able to pick up the instrument and feel accomplished with their progress. While there is no age limit to begin playing the violin, I have seen a continuing pattern throughout my time as a violinist. I have noticed that musicians who perform at a very high standard are those who commence private lessons at a very young age. I therefore believe that the best time for one to start a musical instrument is between the ages of four and six.

When looking at professional, well known violinists such as Itzhak Perlman, Hilary Hahn, Anne-Sophie Mutter, and Sarah Chang, one can see a clear pattern; they all started private lessons at the age of five or younger.
There are many theories as to why musicians are more advanced if they begin playing a musical instrument at a younger age. One is simply that children have less stressors and more time. I myself practiced violin with my mother for an hour a day when I was five. As I grew older, I tried to practice for a longer period of time. By the time I finished college and started working, I found that I was consistently preoccupied by a variety of stressors.
This left almost no time to purely focus on the idea of practicing without worrying about other aspects in my life. If I had not practiced for hours as a young child, it would have been a challenge to improve and perform violin at the level that I do today. Another simple contributor to children’s progress as musicians is that young students have many opportunities available to them while non-professional adult musicians do not.
There are a variety of intensive camps, school and community programs, and classes available for certain age ranges. Many of these are targeted towards young musicians. Additionally there are various opportunities for young students to play in youth symphonies and audition for scholarships at universities.
These are all opportunities that give young students an initiative to practice and therefore help them improve. Many adults are working full time and are not available for these. Other than having the ability to perform in studio recitals or possibly join a community orchestra, there are not as many classes aimed towards their age groups or opportunities to explore what it is like to even join an ensemble and perform with others for the first time.
Lastly, there are many studies that show improvement in attention span and memory of those who begin instruments at a young age. An article written by a science writer in 2020, spoke of new evidence that showed how “musically trained children perform better at attention and memory recall and have greater activation in brain regions related to attention control and auditory encoding, executive functions known to be associated with improved reading, higher resilience, greater creativity, and a better quality of life.”(Maryam Clark, 2020)
This article was written based on a conducted study where musical and non musical students were tested on their attention and working memory. Children have an easier time remembering what they are learning. This simply gives them a huge advantage to adult learners. Younger violin students have more time to practice and remember what they are being taught.
There is no “correct” age at which to begin the violin.
The best time to begin is when one has interest in learning and will take the time to practice and improve. However, if one has the goal of becoming a professional in a symphony or performing in a professional ensemble, this goal is most easily reached if one starts at a young age.
Younger students simply have more opportunities open to them and more time available to practice. Having that said, the ability to play music brings joy to ones’ life whether starting at a young or old age.
A time constraint, stress or preoccupancy should never prohibit someone from learning if they are truly passionate.
Sources
https://blog.frontiersin.org/2020/10/08/neuroscience-cognitive-benefits-musical-education-children-memory-attention/