You file according to your situation as of December 31, 2020. (Child yes, spouse #2).

If you were in a business with spouse #1, things may be complicated.  But for a personal return that does not include a schedule C business or farm or something, this is straightforward. 

also, without Baby's social security number entered the software won't work correctly

there is a weirdly asked question about support asking did THE CHILD provide more than 50% of his support - answer NO.

you should see the $1100 of stimulus for the child on Line 30 of Form 1040 (unless your income limits the payment)