The short answer is it depends. You can longer launch a site, optimize your title tags and start ranking within a few weeks. Google ranks relevant sites that have built authority with their content and other SEO efforts, so it takes time for a site to perform organically.
Typically, it can take anywhere from six months to one year. The amount of time it takes relies heavily on the number of resources you put toward your SEO strategy, the level of competition you are up against, and what your competitors are doing.