This is a weird case where you could claim your girlfriend but you may not claim her daughter. Since you cannot qualify for head of household or earned income credit for the child, it is probably best for the mother to claim her child.
You can’t claim a person as a qualifying relative dependent if they could be claimed as a qualifying child dependent by another taxpayer. Your girlfriend is a taxpayer this year because even though her income is low, the fact that it is self-employment income means that she must file and pay self-employment tax. Since your girlfriend’s daughter meets all the tests to be a qualifying child dependent of her mother, and because her mother must file a tax return for 2020, then you can’t claim the child as a dependent. Then, if you claimed the mother as a dependent, she could not claim her daughter either, because someone who is a dependent can’t have dependents, and that would mean that no one could claim the daughter.
So in this situation, I think the mother needs to claim the child as a dependent and you don’t claim either of them.
