No, you absolutely cannot take this route. You don't apply for an ITIN if a SSN application is in process. One of the requirements to get an ITIN is ineligibility for an SSN. If you are a US citizen, your baby is eligible for an SSN and is hence not eligible for an ITIN.
Also, the ITIN process would take months. It may also be difficult, as you are overseas and may need to mail sensitive documents to the IRS to apply. Either way, you can't apply- I just wanted to emphasize that an ITIN application is not quick or even especially easy.
It is honestly best to wait it out. You could file your tax return and then amend to add the baby, but it is highly recommended that you fil the whole thing correctly the first time.
