CDL said it, western, particularly US culture, over emphasis' the dating thing, I think you should only "go out" with this girl if she is like pretty (wait for it ladies)-up-there for marriage material (there you go, no harm intended
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Becoming friends is a way better way of getting to know someone without all the strings, plus you can then tell if you like her or not after u know her abit better.
Its early days i know but... your wife is your best friend, not some girl who you had a crush on, know what i mean.
Get to know her as a friend first, thats my advice, and hey the chase is always fun