Why do you not have a SSN or a Tax ID? Is the childcare provider refusing to give it to you? They may not want to give out their Social Security number, but they can get a Tax ID instead if they are worried about identity theft issues.
https://www.irs.gov/individuals/international-taxpayers/taxpayer-identification-numbers-tin
https://www.irs.gov/businesses/small-businesses-self-employed/how-to-apply-for-an-ein
If they are refusing to provide the information because they do not want to pay tax on their earnings:
When a childcare provider will not give you a SSN or Tax ID
If they still refuse to provide an EIN or SSN, send your provider a W-10 (Request for Taxpayer Information and Identification Number). You can get a copy of the W-10 by clicking here: W-10 Form & Instructions Complete as much of the form as you can and send it via certified mail (after making copies for yourself).
If the provider does not respond within 10 business days, you can still file your return. However, you won't be able to e-file. Print and mail in your return, along with an explanation and a copy of the W-10 you sent your provider.
(And you might need to start looking for a new childcare provider....)