we expect a new baby and the delivery will be in Canada, the mom is USA citizen but she did not spend 5 years inside and the dad is a green card holder.
You can if you wish, but it won't be of any use for citizenship transmittal purposes as far as you are concerned. Mom needs to file for your immigrant visa with the US consulate in Montreal, and once you are admitted in LPR status, file for your N-600 in the US.
Behar Intl. Counsel 619.234.5962 Kindly be advised that the answer above is only general in nature cannot be construed as legal advice, given that not enough facts are known. It is your responsibility to retain a lawyer to analyze the facts specific to your particular situation in order to give you specific advice. Specific answers will require cognizance of all pertinent facts about your case. Any answers offered on Avvo are of a general nature only, and are not meant to create an attorney-client relationship.
You need a lawyer before you do anything. Do yourself and you family a favor. Find one and soon. You assume we know you facts here. Based on what you wrote in your post, it is impossible to answer this question. As a general matter an affidavit can be used as evidence. Whether it will be given a lot of weight is up to the officer working the case.
NYC EXPERIENCED IMMIGRATION ATTORNEYS www.myattorneyusa.com; email: firstname.lastname@example.org; Phone: (866) 456-8654; Fax: 212-964-0440; Cell: 212-202-0325. The information contained in this answer is provided for informational purposes only, and should not be construed as legal advice on any subject matter.