The biological father's consent to the adoption is not required if there has been a period or one year or more in which he has either failed to have contact with the child or pay child support.
While from your post it does not appear that paternity was ever established, if had been you will still need to give him notice. If paternity was not established, you will need to have a check of the putative father's registry to see if you need to provide notice.
Even if the biological father's consent isn't necessary, or your do not need to give him notice, if he is willing to sign a consent it may be helpful to go ahead and have him consent.
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As a general rule the parental rights of a biological parent must be terminated as a precedent to adoption. Where, however, the mother and bio-father were never married and the bio-father never established himself as the legal father, there may be no parental rights to terminate. A consultation with local experienced family counsel would be wise.
Best wishes for an outcome you can accept, and please remember to designate a best answer.
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Since your facts as stated do not indicate that you were married to the biological father at birth, and since no visitation or support is mentioned I am guessing no paternity was established, therefore you would not have to get the biological father's permission. Probably you do not even "have" to involve the biological father at all.
However, it also seems he would be willing to consent/sign a form, and that would certainly be the A+ way to go.
With or without biological father's consent this would be a very simple process for you.
Best of Luck!