As was mentioned, if she is married, then "Single" is not an option.  She would either be Head of Household, MFS, or make an election to treat the spouse as a Resident to file as MFJ.

What is your actual question?  Are you asking if the children need a SSN number before the due date of the return in order to claim the Recovery Rebate Credit?  If so, the answer is "yes".

The law for the Recovery Rebate defines "valid identification number" by pointing to Section 24 for the definition.  Section 24 requires the SSN to be received before the due date of the tax return (which is from the PATH Act).