No one has access to your accounts or your returns. Do you remember how to access your account(s)?
Many people have multiple TT accounts and forget how to access them. Log out of the account you are in now.
Account recovery
https://myturbotax.intuit.com/account-recovery/
https://ttlc.intuit.com/questions/1901535-forgot-your-turbotax-online-user-id-or-password
Or did you use the desktop version of TurboTax? If so, the files are on your own hard drive or any backup device you used like a flash drive.
https://ttlc.intuit.com/questions/1901486-how-many-turbotax-accounts-do-i-have
https://ttlc.intuit.com/questions/1901535
https://ttlc.intuit.com/questions/1901659-find-your-tax-data-file-in-mac
https://ttlc.intuit.com/questions/1900721-find-your-tax-data-file-tax-file-in-windows
To get a copy of your previously filed returns prepared with online TurboTax https://ttlc.intuit.com/questions/1900748-how-do-i-get-a-copy-of-a-return-i-filed-in-turbotax-online
If you're asking TurboTax to outright furnish you someone's SSN, they are not able to do that. If you're asking how you can get a copy of a previous return you prepared in Online TurboTax, we can tell you how to download/print a copy.
Other ways to find your son's SSN would possibly be on school enrollment papers, insurance applications, healthcare records, etc.