Yes, you may still claim the child and dependent care credit when you're missing the provider's Social Security number or other taxpayer identification number by demonstrating due diligence in attempting to secure this information.
If you file your return claiming your daughter as a dependent and don't provide her Social Security number (SSN) on your return, the IRS will not allow you to claim her as a dependent.
If you are eligible to claim the child as your dependent, and you don't have the child's SSN, then you will need to request an ATIN in order to claim the child as a dependent and (if eligible) to claim the child care credit.
If your non-citizen child dependent does not have a Social Security number (SSN), you'll need to obtain an Individual Taxpayer Identification Number (ITIN) from the IRS for him or her.
If you are a nonresident of the U.S., you cannot claim the standard deduction. However, students and business apprentices from India may be eligible to claim the standard deduction under Article 21 of the U.S.A.-India Income Tax Treaty.
In certain situations, you can claim your nonresident alien spouse as a dependent if they have no gross income and aren't a US citizen or resident. This allows you to use the head of household status. However, your spouse must have an ITIN, and you must provide over half of their support.