I think there is huge value in starting early, in terms of the child doing brain-stretching complex stuff that takes time away from vegging in front of Peppa Pig and Paw Patrol. Particularly if parents have time and willingness to practise with the child, and if there is more to practice than "now play your scales like teacher said" - playing games, clapping rhythms, singing words to tunes learnt on the instrument, playing extra stuff from other books. Having fun is more important than passing grade exams early on.
However, the child won't necessarily end up better or more advanced by starting aged 3 rather than age 7 or 8, and with the wrong teacher (typically ones who like preparing docile older children for exams but don't like teaching kids who make little progress but enjoy it) might get put off. So you have to be realistic about age-appropriate progress and find a teacher who is happy to muck about with a little kid rather than just wanting exam results. And ideally practise/do extra stuff with your child. Music teachers should be able to recommend plenty of good books full of extra material.
Also consider what instrument a 3 year old can learn without too much frustration. A violin might require too much coordination of fine and gross motor skills and intonation and reading and concentration for most (and is expensive to replace when flung across the room). Piano is easier (doing different things with each hand and reading two lines is not necessarily too hard if introduced gradually). Recorder is easier still (there are smaller sizes than the descant used in schools if descant is too big), and cheapish plastic ones are good these days.
Starting with one instrument makes it easier to move to something else when coordination, concentration and endurance are all more developed in a few years (and progress will be way faster)