"recently" to me is 2020. if born in 2020 you can not claim the child until you file the 2020 return in 2021.
make sure you get an SSN for him. you'll need it to claim him. the same with the stimulus - you'll get it when you file for 2020
if he's a qualifying child, he would need over $12,000 in income before a return would be required. kind of doubt that would be the case.
