Children born in 2020 were not included in the 1st stimulus because those checks were based on 2018 or 2019.  But on your 2020 tax return you can claim your child born in 2020 for the stimulus money, as well as the other child-related credits.  When you go through the screens in My Info make sure to say your child lived with you the WHOLE year.    

The stimulus check is an advance on a credit you can receive on your 2020 tax return.  If something went wrong or you did not get the stimulus check this year, you can get it when you file your 2020 return in early 2021—if you are eligible.It will end up on line 30 of your 2020 Form 1040.

https://www.irs.gov/newsroom/economic-impact-payment-information-center-topic-j-reconciling-on-your-...

https://www.irs.gov/coronavirus/coronavirus-tax-relief-and-economic-impact-payments-for-individuals-...

https://ttlc.intuit.com/community/tax-topics/help/how-will-the-stimulus-package-impact-me/00/1393859

At this point, we do not know yet what the new stimulus bill will mean in terms of changes to the 2020 Form 1040, software programming, software updates, etc., etc.  Do NOT be in a hurry to file your 2020 tax return until more is known. Give some extra time to the IRS and the software programmers so that the software can handle the new 2nd stimulus, so that you can get it all by filing ONE time.   It is never a good idea to file early, and it would be especially foolish to file an early 2020 return.

You will not need to do anything other than listing the baby's name and social security number on your return.  Make sure that the name and social security number match exactly what is on the baby's social security card.

There has been some information posted on social media that you can claim a baby born in 2020 on the 2019 stimulus.  That is not true.  You will only get the 2020 stimulus for that baby when your file your 2020 return.

Also, at this point the Turbo Tax software will only reflect a credit for the 1st stimulus.  Suggest being sure it is updated before you file to reflect the 2nd stimulus.  The filing window doesn't open until the end of January, so fingers crossed Turbo Tax has it updated by then. 

Since this affects line 30 of the form 1040 the current availability date of 1/7  for the 1040 is bound to be extended as the IRS still has the newly updated 1040 in draft mode ... once it goes live it usually takes another 2 weeks for the electronic format to be implemented.   I suspect that it will not be ready until sometime mid January which co insides with the stoppage of the second stimulus payments.   Anyone not getting the second payment will then be able to add it to the 2020 return.   NO ONE should ever file before the IRS starts processing returns because of possible complications with the last minute program changes.