If they have a birth certificate then they are already in a database. And if they have no SSN and no Birth Certificate... then you have screwed them for life.
A SSN is only require for them if we claim them as dependents and we don’t. They can get one when they start to work if they want to do that. They can also opt out and just get a taxpayer ID number as a SSN alternative.
We live in Wyoming and this is all very common around here.