What is the legal ruling in Islamic law regarding a child born out of adultery with a married woman before Islam, and what is the possibility of considering this child legitimate, given that the husband is aware of his and his wife's disbelief and wishes to keep both the child and his wife?

Islam erases what came before it, and you bear no sin for what has passed, now that Allah has guided you. The child is not your son, and you bear no responsibility towards him, for the child belongs to the bed [of marriage] and follows the husband, unless he disavows him. Begin a lawful marital life.