How did Madara read the Uchiha's Stone Tablet about the history? Madara said that finding out the history of shinobi is the reason he felt hopeless and left the village. And he learned it from the Uchiha's stone tablet.

But it was said before that the Rinnegan is also needed to read what is written on the Uchiha's stone tablet. So, if Madara only awakened the Rinnegan after he left the village and his final battle with Hashirama, how was he able to read the stone tablet without the Rinnegan?
It's not a stretch to think that he managed to sneak back inside the village and read it in his spare time.

Somewhere before he connected himself to the Gedo Mazo and after he awakened the Rinnegan.

It is not explained however, so any answer you'll get here would be speculative.

EDIT: Now I understood your question, however, nothing told you that the part about the God Tree is only readable by the Rinnegan, maybe it was a part of the tablet that could be read using a Mangekyo.