Can I claim my girlfriend as a dependent without claiming the advanced child tax credit that she received?

If you claim her as a dependent then she cannot claim a child as a dependent and would not be eligible for the Child Tax Credit.  Unless you are the biological parent of the child then you can claim the child on your tax return.

You never enter or report the advance Child Tax Credit anyone else got.   If you claim her and the child you might get the full Child Tax Credit on your return.   She might have to file her return as a dependent and might need to pay the child credit back.   

You can only claim her if she lived with you the whole year and had less than $4,300 total income.

Who can I claim as a dependent?

https://ttlc.intuit.com/community/credits-and-deductions/help/who-can-i-claim-as-my-dependent/00/26781