You should get the 1st and 2nd Stimulus payments for him on your 2020 tax return. Did you already file? It should be on 1040 line 30 if you qualify for the $1,100 (500+600).
Did he show up as a child and get the Child Tax Credit? If not you may need to amend. Did you say he lived with you All year? A child born (even on Dec 31) is considered to live with you the whole year. So pick the Whole Year at the top of the drop down box.
