If you file your return claiming your daughter as a dependent and don't provide her Social Security number (SSN) on your return, the IRS will not allow you to claim her as a dependent.

Two things to consider:

1. If you file your income tax return without claiming your daughter as a dependent with the intent to amend your return on Form 1040-X, Amended U.S. Individual Income Tax Return when you obtain her SSN, you would need to obtain the SSN and amend before the due date for you to be eligible for the earned income credit (EIC) with a qualifying child and/or the child tax credit/additional child tax credit (CTC/ACTC).
2. Filing a Form 4868, Application for Automatic Extension of Time to File U.S. Individual Income Tax Return, would give you an additional six months to file your return, allowing more time to get your daughter's SSN. With an extension in place, you can file an original return claiming the credits your daughter qualifies for with an SSN assigned before the extended due date. However, any tax owed is due at the original filing due date without the extension.

Your child must have an SSN assigned on or before the due date of your return (including extensions) to be a qualifying child for the EIC and for the CTC/ACTC. However, if you, and your spouse are filing jointly without a dependent, you can still claim the EIC if you meet the other requirements for claiming the EIC. In this instance, you would get the EIC allowed to taxpayers without children, which is smaller than the EIC allowed to taxpayers with children. For more information about taxpayer identification number requirements, see the Instructions for Form 1040 (and Form 1040-SR) and Instructions for Schedule 8812 (Form 1040).