Claiming Dependents Without Social Security Numbers

I resided with my girlfriend and our two minor, non-earning children all of 2020. I paid 99% of household expenses everyday of 2020. I earned $37,000 while she only earned $1150 the entire year. The mother of my children is refusing to hand over the SS# of the two kids out of fear she will lose stimulus payments or other future benefits. She has cut off all communication with me over this. I have been through the e-file process and I have gone over my eligibility with the IRS over the phone. Everyone I have spoken to agrees I am the one who can claim the 3 of them as dependents for 2020. What is the next step I should take to claim them as dependents on my 2020 taxes? Should I file a 3949-A? Should I send in a paper return with a letter explaining why I don’t have their Social Security numbers?