If you didn't get a separate checks last year then it should be on your 2020 tax return line 30 if you qualify for it. You can get both the 1st & 2nd Stimulus amounts no matter when your baby was born in 2020. It should be 500 for the first one and 600 for the second round. So $1,100 total.
Did you add your baby under My Info? Be sure when it asks how long your child lived with you that you pick THE WHOLE YEAR (which is acceptable for newborns) and not just the number of months. Go back and double check that.
Did you enter the amounts you did get on the Stimulus screen? There should have been 2 boxes to enter the amounts. To get to the stimulus questions in TurboTax at any time, you can search for stimulus and use the Jump to link.
Generally, if you have adjusted gross income up to $75,000 for individuals and up to $150,000 for married couples filing joint returns and surviving spouses, you will receive the full amount of the recovery rebate. For filers with income above those amounts, the payment amount is reduced.