It depends on the quality of the links,It will need you to do a lot of seo thats not mean over optimization..just do quality post and try to good way building backlinks but remind should be your blog content regularly updated
If I understand your question correctly, just as stated above, you might be ranked within a matter of days. Now if you are asking if you will be ranked well in Google, that is another thing. Primarily to rank well in Google, it will require time and patience and hard work. On Google's webmaster page it states" In general, webmasters can improve the rank of their sites by increasing the number of high-quality sites that link to their pages. For more information about improving your site's visibility in the Google search results, we recommend reviewing our Webmaster Guidelines. They outline core concepts for maintaining a Google-friendly website."
No one can tell you how long it will take to rank since there are so many factors to look at. One thing that will "speed it up" will be based on the keywords you are trying to rank and the competition for them.
Based on that though lower searched keywords may get you to #1 but at what cost when no one may be searching for that term. SEO should never be looked at as how long or how quick as it should be a part of your long term goal.
I'm sure that this question haven't any optional answer . There are a lot of things that can help or hurt to your website and so you don't know when Google will give rank to your website .