"I’m being told I need to file that credit right now" may only mean that you can reduce your income tax withholding from your work pay, because of the addtional tax credit. If so, submit a new form W-4 to your employer. Otherwise, as others have said, you do not claim the 2022 child tax credit until you file your 2022 tax return in early 2023. The rules were different for 2021. You cannot claim a 2021 tax credit for a child that did not become your dependent until 2022.
You said "I’m adding a new dependent". It matters when that child became your dependent. To be a "qualifying child" dependent, for the child tax credit, that child must be related to you and live with you for more than half the year.
