Suzuki starts as early as 3 or 4 and doesn't have to be limited to violin. Cello is much easier on the ears, for example. Suzuki Book 1, regardless of instrument, hsa tunes that are easily adaptable to traditional folk acoustic instruments and make for good opportunities for family music making if family members have even rudimentary playing skills.

But this thread started with reference to a one-year-old, and that's a world of difference from a child who is 3. At 1, I'd foucs on music play comprising singing along together and clapping in time to the music, banging on anything that keeps to the beat, and littering the house with old and non-precious instruments of any kind that a child can pick up, embrace, and play with...and that are of such quality that you won't worry about having destroyed in the course of experimental play.