You will not be able to claim your child on a tax return without a Social Security number. Sort out the problem with Social Security before you file a return. If necessary, get an extension that will allow you to wait until mid-October to file your tax return so that you can get the SSN and file correctly to get the child tax credit etc.
To Replace a Child’s Social Security card
https://faq.ssa.gov/en-US/Topic/article/KA-02723
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