Should I amend previous years if my family just became permanent resident, in order to get credits if I supported them?

I think that you are referring to the Child Tax Credit, the Additional Child Tax Credit and the Credit for Other Dependents.  Is that correct?

Refer to the IRS 2024 Instructions for Schedule 8812.  The instructions state:

If you have a qualifying child who does not have the required SSN, you can’t use the child to claim the Child Tax Credit or the Additional Child Tax Credit on either your original or an amended 2024 return. The required SSN is one that is valid for employment and is issued before the due date of your 2024 return (including extensions).

So, if the children did not have a Social Security number issued before the due date of your 2023 Federal 1040 income tax return (generally, April 15, 2024), an amended tax return would not be able to claim the Child Tax Credit or the Additional Child Tax Credit.  Note 'including extensions'.  Was the due date for your 2023 Federal 1040 income tax return extended because of a Federally mandated disaster declaration?

The instructions also state:

If your qualifying child does not have the required SSN, but has another type of taxpayer identification number issued on or before the due date of your 2024 return (including extensions), you may be able to claim the Credit for Other Dependents for that child.

Did your 2023 Federal 1040 income tax return report the Credit for Other Dependents for the children?