While it's never confirmed whether Bill is Sophie's biological father, there are a few clues throughout the first movie that suggest he is. During his first conversation with Sophie, we learn that she is actually named after his great aunt, Sophia. In another conversation at Sophie's bachelorette party, Bill asks how Donna was able to afford her place and Sophie reveals she got the money from his aunt Sophia. Bills then adds, "I always heard her money was left to family." Of course, since Donna herself doesn't know who the father is, Sophie's name wouldn't really be any indication of her paternity.
Though, there is one more clue that Bill could be Sophie's biological father. In the first film, Sophie was supposed to sing "The Name of the Game" with Bill, but it was cut from the theatrical release. If the scene would have stayed in the film, it would've been the only duet Sophie sang with one of her potential fathers.