Yes, you can claim credits for your child although you do not have a SSN, as long as the child has an SSN and meets the following requirements:
The child must:
- Be your daughter, son, stepchild, eligible foster child, brother, sister, stepbrother, stepsister, half-brother, half-sister, or their descendant.
- Be under age 17 at the end of the tax year.
- Not provide more than half of their own financial support during the tax year.
- Must have lived with you for more than half of the tax year (certain exceptions exist).
- Be claimed as a dependent on your tax return.
- Not file a joint tax return for the year (except when only filing to claim a refund of withheld income taxes or estimated taxes paid).
- Be a U.S. citizen, U.S. national, or U.S. resident alien.
- Have a Social Security Number issued by the Social Security Administration that is valid for employment.
Here is a TurboTax article about the Child Tax Credit.
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