within 2 months you want to rank your keywords!! it is possible but your work starts from web onpage factors, your must have maximum onpage factor done, in short your site must beat your competitor in onpage factors, then you can start offpage SEO, while diverting traffic towards your site from social media platform as well.
It is always a tough to top site on top but professionals love to get it, my current clients sites have top ranking, in the past i had it for more than 10 website!!