It becomes clear halfway though the movie that The Wizard of Oz, is in fact, the biological father of Elphaba Thropp. When you really start to think about it, you notice the potion he used on her mother in the beginning of the film to get her drunk, is green. It makes sense that she is then cursed with green skin her entire life. It is also no accident that the Wizard requests Elphaba as the one from the school he wants to see. To top things off, he sings a song to her about how he always wanted to be a father. It is crystal clear that The Wizard of Oz is the biological father of Elphaba.
It is only a matter of time in Part Two, before the “secret” comes out of the bag.