I think children can wear sunglasses at any age as long as they don't play with the sunglasses just as a baby often does. Maybe a baby can wear sunglasses to protect their eyes form the harmful UV rays of the sun too if they don't drop the sunglasses on the floor. It will cost us at least $100 to buy a pair of good sunglasses. If they are damaged by accident, it can be a loss. So consider that before giving your child a pair of sunglasses. Good luck!
The UV rays from the sun will damage our eyes. Too much exposure to sunlight will lead to macular degeneration and cataract. While children often play in the outside, so I think we can buy them a pair of sunglasses if they can promise that they won't damage them. During the development of the eyes, what does sunlight do to our eyes haven't been found yet. But I think a pair of sunglasses is good for children' eyes. So we'd better buy them as soon as possible.
A pair of sunglasses can lower the risk of getting cataract and age related macular degeneration in later life. But if your children don't want to wear them, you shouldn't push it. You can ask them to wear a hat or visor to protect their eyes from the sun.
It is said that 80% of all sun damage to the eyes are done before age of 18. But some people said that our eyes can't filter out UV rays before age of 25. However they don't mention that when sunlight damage our eyes, so I guess maybe our eyes are easy to get damages since we were a baby. So we should protect our eyes from the sun when we were a baby. Many parents buy sunglasses for their baby nowadays. You can do that too.
It is never too early to buy a pair of sunglasses for your children. But I still suggest you to buy a pair of sunglasses for your children when he or she is 3 years old. Because he or she can understand your words and follow your suggestions so they won't broke the sunglasses by accident anymore. Before that age, you can buy a brim hat for them to help protect their eyes from the sun.