7 Wonders Duel Pantheon : Can a player invoke a God during Age I?
Yes I believe you can activate a God in Age I using the Divine Theater.  


  During Age I, the players will choose the Divinities they will be able to invoke during Ages II and III.


is taken from the Overview of the rules.  I think that's more just a general guide of what happens rather than a strict rule that prevents The Divine Theater from working.  I think if using The Divine Theater was in some way forbidden during Age I then that should be explicitly stated in the rules.  Note The Gate allows a player to use any god revealed from the top of any deck,  This was not chosen by a player to be able to be invoked during Ages II and III.  So if A God can be played that way (just not following the exact letter of the overview)  then I see no reason why The Divine Theater can not either.

Note your revealing all the cards from a 'Deck' so if you choose a category that only has 2 or 1 card left in the deck that that is all you reveal.  Note you return them in the order you choose, this is relevant for the Gate card.  I would also argue that as the cards are 'revealed' that your opponent will see the order they are returned.