My name isXXXXX'm a licensed attorney. Glad to try and help out.
Sure sorry for the circumstances, truly. My heart goes out to you.
Accordingly, I'll speak plainly rather than doing you good folks the disservice of misleading you or lying. I have every sympathy to your daughter, but I feel you deserve a candid and truthful answer. So, here goes. There are two steps, namely: (1) establishing paternity; and (2) adjudicating custody. In other words, as long as he truly is the biological father (either by admission, such as voluntary listing on the birth certificate, or established by genetic testing), he fully enjoys standing when it comes to parenting matters such as visitation, custody and support.
Regarding the statutory provisions you cited, neither of these strips a biological father of such standing:
Oklahoma Code §104. Support and education.
The parent entitled to the custody of a child must give him support and education suitable to his circumstances. If the support and education which the parent having custody is able to give are inadequate, the other parent must assist to the extent of his or her ability.
Oklahoma Code §106. Custody of child born out of wedlock.
Except as otherwise provided by law, the mother of an unmarried minor child born out of wedlock is entitled to the care, custody, services and earnings and control of such minor.
In fact, the issue of gender preferences has been eliminated in modern jurisprudence, meaning both parents enjoy equal footing in determining what is in the best interests of the child. Now, having said all of that, there are numerous reasons why the relief being sought may absolutely well be denied. But, as to the foundational and prudential issue of legal standing to bring suit, I regret to say it's without dispute that a biological father does enjoy such.
If you have a follow-up question or need clarification, please just say the word by using "reply" to reach me.
I truly hope all works out for you and your family.