You will have to wait until your return has been fully processed in order to amend. The 1040X you will need is supposed to be available by March 25. Yes, you should have said your child born in 2020 lived with you for the whole year. You have to say that for a newborn so that you can get the child-related credits and right now for the stimulus money. You can get up to $1100 of stimulus money for your child, and perhaps the child tax credit and/or earned income credit, and childcare credit. It should definitely be worth the trouble of amending.
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