Remember that even if 30% of the girls there are Greek (and I think it's actually less than that), that means 70% are NOT.
Go here:
http://wow.ua.edu/
Scan the CW for clubs and groups that are meeting. Visit the campus student ministry of your choice. Go to church - LOTS of students do and there are several right next to campus.
Volunteer!
There are lots of ways to make friends at UA!