My son is not eligible to get SSN but he has lived with all 2019 and I believe he will be eligible for new $500 tax credit but TurboTax doesnt show that option?

If your dependent child has an ITIN, but not an SSN, issued before the due date of your 2019 return (including extensions), you may be able to claim the new credit for other dependents for that child.

Credit for Other Dependents

Dependents who can’t be claimed for the Child Tax Credit may still qualify you for the Credit for Other Dependents. This is a non-refundable tax credit of up to $500 per qualifying person. The qualifying dependent must be a U.S. citizen, U.S. national, or U.S. resident alien.