We have successfully ranked some of our clients within the second month for a few keywords.
However, it depends on the "Keyword Difficulty" level too.
You can see in the image below that this keyword "used car dealership" in "New York City" has a Keyword Difficulty score of 13/ 100 and we have seen keywords with this Difficulty Level ranked on the first page with in the first 5 to 6 months.
You can see that this keyword has a total 9000 searches.
Even if you rank on the fifth position of the First Page of Google, youl still be able to get 500 visitors organically out of 9000 searches on this keyword.