You can file without the SSN but you have to file by mail, you can’t e-file. Attach a written statement giving your spouse’s name and any identifying information you do know, such as last known address and date of birth. TurboTax might not even allow you to print a form for mailing unless you use a fake SSN; you can try 999-88-9999 and then erase it or cover it with white out before filing.
