Yes. When your file your 2020 return (not until the end of January) you will put down how much you already got. Then you will get the difference. When you enter your baby under My Info be sure to say baby lived with you the WHOLE YEAR, not just the months since birth.
The first Stimulus Check is really based on 2020 tax return. Any amount you already got will be reconciled on your 2020 return line 30. If you didn't get a Stimulus Check (and qualify) or you qualify for more it will be added to your 2020 return. But the good news is if they paid you too much they won't take it back.
When you go through the federal review tab it will ask how much you got if any. Or to enter your stimulus payment in TurboTax, type "stimulus" (without the quotes) in the Search box, then click the link that says "Jump to stimulus."
When you prepare your 2020 return you will claim your child born in 2020 as a dependent. Enter your child's Social Security number and make sure the child is shown as a dependent at the top of your Form 1040. When it asks how long the child lived with you in 2020 say the whole year. That way you get the child--related credits your are eligible for and the stimulus money. Wait until late February so the dust settles on the stimulus money so you can get all of it on your tax return.
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.