I am stationed in japan and am waiting on the return of my child's passport to apply for her SSN. It is a very lengthy process. Can I file without submitting via mail?

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You can file (paper or efile) anytime without her and amend (paper) to add her when she has a SSN, As military you can get extensions to file See this from the IRS  https://www.irs.gov/publications/p3#en_US_2018_publink100050106