3800: Rome expands, and the tribes in the hut there give us ... Mysticism! First tech i've ever gotten this way.
This changes things a bit; i'll go for polytheism or one of the other religious techs next, instead of animals. We don't want an early worker anyway ...
3760: Discover hunting; start work on Polytheism (12). That's a reasonable length of time for it. Go for Meditation (9) if you want the faster religion, but only do that if you're a civ that starts with Mysticism ... otherwise you'll get beaten to it. Polytheism, on the other hand, is often not gone for right away by the AI, and even if it is, Monotheism is right after that, giving you 2 shots at founding a religion (which is very important to do!).
3720: More exploring; find a hut, and a wheat. That's good, so the stone city can have wheat also, and use those shields