Ok, for starters, this is a ridiculously privileged thing to be able to do, so I want to own that immediately. I wouldn’t recommend it unless you have some extra money and are pretty sure your children will never qualify for need-based financial aid for college (US centric here).
I set up an investment account for each kid at Vanguard. I funded the the initial 3 k. Any money they choose to put in, from their allowance, cash presents, forgoing school lunch, dog walking, etc., I match 100%.
Why? Well, I am a big believer in compound interest. Starting investing, say, at age 8 offers decades of extra compound interest.
It also normalizes and incentivizes the fuck out of saving and investing. Two of my kids skip getting school lunch once a week at $5 a pop. That $20 becomes $40 a month for their respective accounts. My other child opts for the weekly lunch, but just handed me $400 from her afterschool job and I dropped $800 into VTSAX on her behalf. That kid is ten years old. I am pretty sure these saving and investing behaviors are getting deeply internalized at a young age.
Moral qualms, this is one more way that people with money (me at the moment) can transfer wealth between generations and solidify privilege.
Edited to add: would you consider doing this for your child? Why or why not?