Firstly, is faith something you can know, or something you can have?
Secondly, your reasoning is faulty, as mike said, how can you have eliminated all other possible answers.
Thirdly, you wrongly assume that we categorically refuse to come to a conclusion which involves god. I'm not going to state that believing in god is a particularly illogical conclusion, I'm just saying it's one of many pretty illogical conclusions. I happen to really enjoy the massive variety and interesting features of all sorts of illogical conclusions without fetishising some sort of ultimate answer because, and I will happily admit this, I don't think I've ever going to properly work it out.
( TFD is sporting this season's finest necropants, Thu 6 Oct 2011, 2:25, archived)

faith is something one has, I guess, but one knows it when one has it.
I can eliminate answers by mutual exclusivity. There are four possible ways for the universe can exist, and three of them are absurd. Add to this list if you can think of any others, by all means.
1. circularity
2. infinite regression (turtles all the way down)
3. absolutism or "skyhook" i.e. "it just is"
4. self-reference

Thirdly, I'm not addressing you in particular on that one.
( Moon Girl Technologies horrendous beanbag, Thu 6 Oct 2011, 2:35, archived)

5. god made it.
6. someone shat it out of their arse

Both of these possibilities are equally possible.
( mike woz ere 7442200 & 7696970 getter, Thu 6 Oct 2011, 2:39, archived)

5=2 "gods all the way down" (who made god?)
6="god made it by accident"=2

or =3 if you prefer to say that "god just is".
( Moon Girl Technologies horrendous beanbag, Thu 6 Oct 2011, 2:45, archived)