Joel
*Maury voice* You are not the father!.
All who guessed it is right and here's why. The moment Alex woke up from the coma Charlie got a visit from another spirit telling Charlie she isn't fully back now with this info it started revealing this cryptic message which lead to their break up and then in the season finale after she gave birth and charlie held the baby all her memories and time with Charlie came flooding back which answered the cryptic message that the spirit told Charlie.
The thing that was missing a part of Alex was motherhood that somehow was left behind in the spirit world which i assumed they talked bout having a child before the series even started. With her motherhood returning the moment she hands off the baby to Charlie indicating he is the father and if he wasn't the father Alex wouldn't say I love you charlie she been still drawing a blank lol.