From an SEO perspective, it is virtually impossible to rank for medium/high keywords in less than 1 month. But it is totally possible to rank for long tail keywords that have low competition.
What I would advise you to do is:
1) Compile a list of long tail keywords, with low competition. (Keywords getting 10-50 searches/mo with less than 5,000 competing pages "Exact Match")
2) Write a couple of articles on your website focusing on these long tails.
3) Build lots of links to those pages. (Use a mix generic anchor text and naked URL! Spammy links in that case will work if this is a burn and churn website)
4) Wait for a week or two and you will be ranked on top of page 1, if not #1 for your long tails.
Good luck.