No. She did not live with you long enough. The general rule is the child must live with you more than half the year. For a new born she must live with you half the time since being born.
The other issues, paternity and support, are not relevant if the residency test is not met.
While it's true that child can be the “qualifying
child” dependent of any close relative in the household, e.g. a grandparent; they must share that home for more than half the time to qualify for CTC and EIC
