WebKit was forked from KHTML. Chromium used WebKit, until Blink was forked. All of that was only possible because the browser engines are open source.

As with anything, you always need somebody (or a group of somebodies) to help something new gain traction. There's no magic pixie dust that will let you develop a major new platform without commensurate resources. What open source does do is lower the cost of entry and make it easier to build up to a level where you can make an impact.