It took Google just 4 days to index my brand new website without submitting it to any search engine, I did some other stuff tho. How long did it take before Google indexed your website?
I`d also say 3 - 4 days to get indexed is the normal time. Fastest time i`ve got a new domain in the search listings was about 6 hours, but that what through link linking on high traffic websites.
I`ve had a new blog post indexed and ranked in little over an hour.