The mere fact he gave up on the mediation and has not see the child for seven years is not, of itself a reason he cannot have access or custody.
If he makes an application to the court for access/custody even now, the court will generally be willing to grant some such access as the courts decide such matters on the basis of what is in the best interests of the child and will generally accept it is in the interests of children to have or develop relationships with both their parents. This presumption can be rebutted if there is evidence of genuine issues which convince the court that it is not in the child's interest to have such contact, but that will generally be limited to situations where the father is violent, abusive or has some serious drug addiction or mental illness or similar.
Setting aside such possible exceptional circumstances, the fact he has been absent for many years means that even if he is successful, a court would likely only allow him very limited access initially so as not to introduce him into a young childs life in an a traumatic way.
Taking the above into account, and assuming there are no exceptional reasons, you should consider negotiating, either directly or through further mediation, for a gradual introduction to him, supervised by you or another trusted family member with a view to expanding this to something more signficant as the child's comfort level with her father increases. How far this should progress will depend on how well things develop, and if you cannot agree by negotiation or mediation, the courts can decide the matter ultimately.
I appreciate this may not be the answer you were hoping for but it does reflect the law as it applies to your situation.
Good luck and please rate my answer.