Why can I not claim my baby on my taxes without a SS#

[DoninGA]

The US Tax Code requires that to claim a dependent on a US Federal tax return, the dependent must have either a SS number or an ITIN issued by the IRS.
Have you applied for a SSN for the child?

[Lisa995]

Hospitals nowadays have you apply for the SSN right there in the hospital before you leave.  If this didn't happen you need to go to the local Social Security office and apply for one yourself.

[Opus 17 · Accepted solution]

Because that's the law.

Don't file without the dependent and then amend later, because you can't get the dependent benefits that way either.  You must have the child and their SSN on your original "timely filed" tax return.  If you can't get the SSN before April 15, you will need to file for the automatic extension.