Is there a way to put child on taxes if I haven’t received her social?

No.  To claim a child as a dependent on a tax return they must have a Social Security number.  Wait for the SS number since you can file your 2021 tax return at any time if you have a tax refund on or before April 15, 2025.

See this additional IRS guidance: https://www.irs.gov/faqs/filing-requirements-status-dependents/dependents/dependents-9

If it comes to this point, you may file an extension for your taxes. PS: It was taking roughly ~2 months to receive a Social Security Card for a newborn over the summer.