how to increase my web site rank in a week?

You should do some website optimization such as buy traffic, backlinks and etc but it is impossible to do that in a week
As said above, a week is not enough and the process may take few months. Just have patience and learn more about SEO and you'll get there.
alternatively, you could consider ranking a YouTube video or something, which can actually rank in a week. Google loves YouTube videos
You could not get to top in a week its a process with relevant blogs and high quality content that are updated regular basis to reach on SERP and there are many other techniques preferred for doing OFF-page,please do refer to that.
You need to get some really good backlinks that have high authority in google's eyes, and when google crawls the site/link in that period of time, there's big chance you get credited for having the link. Alternatively, some fresh news on a news site, youtube video or google hangout could pop up fast, but that's like a hit or miss IMO.
I'd go with :

1. SEO
2. Social media
3. GEO you want to target
4. Great recent content (trending)
5. Blackhat SEO (obviously) --> using Google trends keywords given.

Good luck !
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