There is nothing else for you to do. The fist and second stimulus payments were reconciled on your 202 tax return, which would have provided the additional amount for your newborn.
Any additional stimulus will be based on your 2020 tax return, including your newborn, once they prepare to send out any future payments in the third round of stimulus.
**Say "Thanks" by clicking the thumb icon in a post
**Mark the post that answers your question by clicking on "Mark as Best Answer"