In March 2006, KinderStart filed a lawsuit against Google over search engine rankings. KinderStart's website was removed from Google's index prior to the lawsuit, and the amount of traffic to the site dropped by 70%. On March 16, 2007, the United States District Court for the Northern District of California (San Jose Division) dismissed KinderStart's complaint without leave to amend, and partially granted Google's motion for Rule 11 sanctions against KinderStart's attorney, requiring him to pay part of Google's legal expenses.
Advertising with Google won't have any effect on your site's presence in our search results. Google never accepts money to include or rank sites in our search results, and it costs nothing to appear in our organic search results. Free resources such as Search Console, the official Webmaster Central blog, and our discussion forum can provide you with a great deal of information about how to optimize your site for organic search.
Other research shows that exact-match domains that are deemed to be relevant, valuable, and high-quality can see a ranking boost because of it. However, if you already have an established website, you don’t need to go looking for an exact-match domain for your business; focus on a URL that reflects your business and optimize the heck out of it instead!