No 国籍冲突。

remember my following. will help you and others in the same situation:
1. no any citizenship conflict for this child.
2"取得中国国籍，同时丧失美国国籍；" wrong for this case.
this child has chinese citizenship without lost US citizenship. (can still has US passport. can apply/renew US Passport anytime without to wait to 16 or older. even this child don't hold US passport, He/She still has US citizenship)
3. go to US consulate office to APPLY us passport. Not to restore US citizenship. because he/she never lost the citizenship.
("持美国出生证原件去美国领事馆申请恢复美国国籍")