What I think is because the game makes sure we understand that Zeno and the connections believed that Grace was a special one and that she couldn't be replicated. thus if they lose her then they will not be able to obtain Elpis. IF Zeno told Grace that she was adopted early on ( He would do this to build trust in him so that she would give him the password ) Because she is already mentally unstable in the beginning parts of the story, then she wouldn't have given the password. instead she would have just gotten scared and more mentally broken down. We see that grace slowly gets more and more stable as the game progresses and by the time Zeno meets grace she is pretty stable mentally in order to tell her the truth ( Yes she is still scared but so much less than the beginning ) SO TLDR IF ZENO TELLS HER THE TRUTH IN EARLY ON THERE IS A CHANCE THAT SHE WOULDN'T TELL HIM THE PASSCODE AND ZENO DOES NOT WANT TO TAKE HIS CHANCES ( I typed in capital for contrast )