How would request a PDF of my kids social security numbers if I never received them after birth?

Visiting your local social security office is quick and easy. You can also go online. Please see SSA FAQ for SSN cards here.

Did you apply for the SSN?  Often, someone at the hospital will do that for you, but not always.

You should not file a tax return until you get the SSNs, even if it makes you late.  Be sure to get the automatic extension in that case.  If you file without the SSNs and then go back to add them later by filing an amended tax return, most child tax credits won't be paid.  Most child tax credit are only paid if you file an on-time tax return containing the children's SSNs.