No, You can't get the ADVANCE payments, for a child born in 2021, but you'll be able to account for your child when you file your 2021 return next year. Provided you are otherwise eligible to take the child credit, you can take a child tax credit of up to $3,600 for your baby on your 2021 Form 1040.
There has been talk about the IRS updating their portal to allow advance payments, in your situation. But, to my knowledge, that has not happened yet (and probably won't).
The IRS was supposed to update their portal Manage Payments so a child born in 2021 could be eligible for the monthly Advanced Child Tax Credit payments in 2021. This has not happened and there is a good chance it will not happen this year.
Go to this IRS website for the portal - https://www.irs.gov/credits-deductions/advance-child-tax-credit-payments-in-2021
Go to this IRS website for information concerning the portal updates - https://www.irs.gov/credits-deductions/2021-child-tax-credit-and-advance-child-tax-credit-payments-t...
You will be able to add your child as a dependent on your 2021 tax return and if eligible receive the Child Tax Credit on your 2021 tax return.