If the baby was born i9n the U.S. then you absolutely must have an SSN in order to claim them as a dependent. As I understand it, that baby couldn't even have left the hospital without the parent first having completed an application for an SSN. But then I don't know your situation. If the baby was born "a couple of months ago" then you should have received an SSN card for the baby by now.
If you did not yet apply for an SSN for the child, then you need to visit your local social security office on Jan 2 and bring all the paperwork with you from the hospital (or whatever institution the baby was born in) as you will need it. I do know that "some" of the paperwork required will be the original certificate of live birth with original signatures on it, along with other paperwork that I can't recall exactly, which you would have been provided prior to departing the medical facility where the birth took place.
Once you submit your application, you should receive the SSN card in 4-6 weeks, which gives you plenty of time to have it for tax filing, provided you don't procrastinate.
