For reference I'm in indiana

So I had a child back in july, bio dad and I agreed to go no contact at the beginning of my pregnancy as he suddenly "didn't want kids" and even wanted me to get an abortion. We haven't spoken since January. We were never married and only my name is on the birth certificate. I don't even have his number anymore tbh. Right now I habe sole custody, but he never signed away his rights, again his name was never on the birth certificate. If a year or two goes by would he be able to fight for custody? Or would the change be gone due to "abandonment" if so wheres the cut off time? I don't think he's ever going to try to fight for custody but I'm asking just in case so I know what to expect.

Mind you my ex is a complete manipulative narcissist who sees multiple women constantly and that's something I wouldn't even want my child around. My current partner has talked about potentially "adopting" my son if our relationship continues in the long run. Just looking for whatever advice I can get.