No, but keep reading.
Any tax benefits that a person with an SSN might be eligible for that a person without is not, can only be received if you file an on-time tax return after the SSN is issued. There is no way to go back to 2018-2022 and get those benefits by filing amended returns. For your 2023 tax return, you could get the child tax credit if you have not filed yet AND you filed an extension request before April 15. That would mean that if you filed now, it would be "on time" and you could claim the full CTC. But if you already filed your 2023 return, you won't get the CTC by amending.
However, even if your child did not have an SSN, you were still allowed to claim them as an "other dependent" for the $500 credit, and I believe you could get the dependent care benefit if you paid for day care so you and your wife could work. If you did not include your child as a dependent at all, you could amend your return to add your child and claim the $500 other dependent credit, you just won't get EITC or the full CTC.
