I read about a lot of people who ranked their site without building a single link. Does posting great content or building a great site can get you ranked higher? What if I'm in a competitive niche, do I need to build links? Or should I post my content to Social Media and wait for links to be built?

You can even rank better with your social media signals but that wont help for you a long run. If you could six in all the 6 balls, have a try.

No you cannot rank your site without link building. Because Link Buiding only a technique which rank any type of site.