Yes, in many cases, a child born abroad to a U.S. citizen parent automatically acquires U.S. citizenship at birth, but you need to apply for proof.

You can file Form N-600 Application for Certificate of Citizenship if the child now lives in the U.S. or Apply for a Consular Report of Birth Abroad CRBA at a U.S. embassy or consulate if you're still overseas.

The U.S. embassy or consulate is the best place to apply for a CRBA and U.S. passport for a child born abroad.

If citizenship is confirmed, your child is eligible for a U.S. passport often quicker than waiting for an N-600.