I can buy anything for a newborn. Also a domain or a phone number.
The biggest negative is your newborn might not care or want whatever domain you picked out.
So the only real option is to buy tens or hundreds of domains and keep it secret. Then reveal the domain that most closely matched them when they’re of age, whatever that may be.
I have my own domain(s) and my kids could have subdomains as DNS intended ;)
Think like a photo book, but it's public.