When you file your 2021 tax return NEXT YEAR in 2022 you will be able to claim your child who was born in 2021. No you will not get the $1400 stimulus payment that was issued based on a 2020 tax return. But when the IRS portal is fully operational you can enter your information including your baby's Social Security number to start getting the monthly child tax credit payments.
There will be monthly child tax credit payments going out beginning in July 2021, with some of the CTC still left as a refundable credit on your 2021 tax return next year.
No you will not receive $1400 in 2021 for a child born in 2021.