The sooner the better in short.
The younger you can instill the basics of fiscal responsibility and how the system works the better.
Opening a savings account for your child when they are born is probably or should probably be the standard course of action in this fast acting world as their first car, first suit and college education are not going to come cheap later and putting money towards these goals now and letting it grow over time whilst compounding that with more savings is the best thing you could possibly do.
Along the journey talking with your child about this account and finding a way to relate it to real world type stuff so that some day they will have a firm grasp on what true self actualization is and that the most powerful person in the universe is the individual and not the masses then you will have set into motion a plan of such greatness your child could never hope to repay your kindness and wisdom in twenty lifetimes.
Many people who suffer from poor finances do so because they never had a foundation laid properly and that foundation is simply put knowing how to save and how to save intelligently with a touch of wisdom.
This wisdom can and should be handed down from the parents to the child in the form of a children's savings account no matter how small the amount able to be saved the less will be learned and the child can grow to be a fiscal success whilst also enjoying a solid fiscal foundation thanks to their wonderful and caring not to mention wise parents.
Get started as soon as possible even if your counting pennies they do add up very quick as the lesson being learned from the pennies is worth more than any amount of money.
A little research will show every single lottery winner in the history of modern times is filed for bankruptcy because they lacked one common skill across the board, the ability to save for tomorrow.
This quite possibly could be the most important thing besides teaching your child right from wrong.
Save.
Save now.