TurboTax does not have your child's Social Security number.  As the parent you are supposed to keep that on record.  You can get it from a past tax return or from a transcript of a tax return if you claimed the child as a dependent on a previous return.

Access to prior year returns.

https://ttlc.intuit.com/questions/3402465-how-do-i-access-my-prior-year-2016-or-earlier-return

You can get a free transcript from the IRS:   

https://www.irs.gov/individuals/get-transcript

How do I get a copy of a return I filed using online TurboTax?

https://ttlc.intuit.com/questions/1900748

How do I get a copy of a return I prepared using desktop TurboTax?

https://ttlc.intuit.com/questions/1900639

How to upgrade to PLUS

https://ttlc.intuit.com/questions/3404582-how-do-i-upgrade-to-plus-if-i-already-filed-my-2016-tax-re...

https://ttlc.intuit.com/questions/3796106-why-do-i-have-to-pay-to-access-my-prior-year-return

https://ttlc.intuit.com/questions/3355524-when-does-access-to-my-prior-year-turbotax-online-returns-...