How wonderful of you to want to adopt the baby as your own.  Once you are married you need to start the process.  If the biological Father will voluntarily relinquish his rights you can generally do the termination and adoption in the same proceeding.  If he will not then you have to have his rights terminated and that could be a difficult thing.  I understand what you have said about the affidavit and birth certificate but you need to do this by the book or he can try and have the termination and adoption put aside.  Good luck.