Am I still claim my baby even though we do not have his social security number yet?

From the IRS:

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

You have two options:

1. You may file your income tax return without claiming your daughter as a dependent. After you receive her SSN, you may then amend your return on Form 1040-X, Amended U.S. Individual Income Tax Return and claim your daughter as a dependent. Generally, you have three years after the date you filed your original return or two years after the date you paid the tax, whichever is later, to amend your return.
2. The other option is to file a Form 4868, Application for Automatic Extension of Time to File U.S. Individual Income Tax Return. This option would give you an additional six months to file your return; by then you should have your daughter's SSN. However, any tax owed is due at the filing due date without the extension.

You may also be eligible to claim the earned income credit (EIC) and/or the child tax credit/additional child tax credit (CTC/ACTC). Please note that you may not claim your child as a qualifying child for the EIC on either your original or an amended return if your child doesn't have an SSN on or before the due date of your return (including extensions), even if your child later gets an SSN. Similarly, you may not claim your child as a qualifying child for the CTC/ACTC if your child doesn't have an SSN before the due date of your return (including extensions), even if your child later gets an SSN. However, if you have an SSN, but your child does not, 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).rom the IRS: