You cannot claim a dependent unless they have either a SSN or an ITIN. If you are waiting for either of those, request an extension now and file later when you get the SSN.
Remember that an extension does not give you more time to pay. You need to pay your tax due by April 15. The extension only gives you more time to prepare and file your tax return forms.
https://turbotax.intuit.com/irs-tax-extensions/
https://ttlc.intuit.com/turbotax-support/en-us/help-article/tax-extension/need-file-extension-person...
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