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.
You can get a free transcript from the IRS:
How do I get a copy of a return I filed using online TurboTax?
How do I get a copy of a return I prepared using desktop TurboTax?
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