I would be most interested in a Religion that does not hit the 'cause, nature and purpose of the universe' part.
You owe me a religion that doesn't meet any of the additional characteristics as well!
But yeah, I don't know much about different religions, but I would imagine there could be religions that do not have a creation myth, and thus are agnostic towards the 'cause' of the universe.
As for the 'purpose', well, I guess in Christianity it's not clear what the purpose of the universe is, but it is kind of implied that there is a purpose due to the (ill-defined) omnipotence and infinite quality of god, or some such.
However, take a religion where the gods are not omnipotent but rather just higher powers, and where the universe itself wasn't created by gods or anything with a goal in mind, then you probably don't get a statement of belief about its purpose or the existence of a purpose. For example,
here's a creation myth of the ancient Greek:
"Myths of origin" or "creation myths" represent an attempt to render the universe comprehensible in human terms and explain the origin of the world.[22] The most widely accepted version at the time, although a philosophical account of the beginning of things, is reported by Hesiod, in his Theogony. He begins with Chaos, a yawning nothingness. Out of the void emerged Eurynome,[citation needed] Gê or Gaia (the Earth) and some other primary divine beings: Eros (Love), the Abyss (the Tartarus), and the Erebus.[23] Without male assistance, Gaia gave birth to Oranos (the Sky) who then fertilized her. From that union were born [.... bla bla]
I don't see how that would imply any purpose to the universe more than a scientific theory of the origin of the universe would.
I think saying that being an Atheist is believing in something is pretty false. For one thing, it isn't really faith based, since if an ultimate being(s) proved his/their existance and influence, the existance of a soul and so on, then there wouldn't be any athiests, whether or not you think said being(s) is/are good or evil.
Secondly, there is no set of beliefs that are in any way standardised that Atheists follow. An Atheist can believe in anything he/she wishes to, so long as they maintain a disbelief of the existence of gods. Lack of belief is zero, not a negative number, in the same way that dryness is a lack of water.
I don't see how you are bringing new arguments to the table. To restate my own opinion on the matter: There are different forms of atheisms, and
some do indeed involve a statement of belief, not just a lack thereof (e.g., "I believe gods do not exist", "I believe the biblical god does not exist", etc.).
I also don't think confusing things further by bringing "faith" into the discussion is helpful. Yet another term everyone is going to argue about...