The child is automatically and involuntarily a US citizen when the conditions in the law are satisfied, and the mother's consent is not part of those conditions.
Assuming you are a US citizen at the time of the child's birth, and the mother was not a US national at the time of the child's birth, the physical presence requirement is that you must have been physically present, in any status, any time in your life prior to the child's birth, for a cumulative total of 5 years, including 2 years after you turned 14. If the child was born in wedlock, that is the only condition, and no other conditions need to be met. If the child was born out of wedlock, in addition to the physical presence requirement above, as RoboKaren's answer mentioned, certain additional things need to happen before the child turns 18:
- the child is legitimated, acknowledged by you, or had paternity determined by a competent court, and
- you made a written statement to support the child until he/she turns 18
I will assume the child was born out of wedlock for the rest of this answer. The easiest way to satisfy the above additional requirements for a child born out of wedlock to an US citizen father, is for the US citizen father to apply for a Consular Report of Birth Abroad (CRBA) for the child at a US consulate in the country the child was born in, before the child turns 18. As part of the CRBA application (DS-2029 item 28, or DS-5507 part II if the US citizen is not present), the US father of a child born out of wedlock will acknowledge paternity and agree to provide financial support, satisfying the requirements.
7 FAM 1443.1 says that CRBA applications can be made by either parent, and does not have a 2-parent signature requirement (unlike passports which require both parents to consent for children under 16). So you can get a CRBA to document the child's US citizenship, even if you will be unable to apply for a US passport for the child or take her out of the country. 7 FAM 1444.1(b) says that the minor may be required to appear at the officer's discretion, although I would think that that would be less likely since your daughter is so young; if the officer requests her appearance, that might be difficult if you don't have custody of her.