For the case of new websites don’t expect any considerable results in the first six months. If you start a new website and publish top quality content on a regular basis and do your social media promotion, you can expect to see some of your pages in the 2nd and 3rd page of Google in the first 3 months and then gradually some of your pages will move to page 1 after the 6th month.
This will probably not get you high amounts of traffic but it is a sign that what you are doing is in the right direction.
If you keep pushing by getting more pages indexed and also a few natural links from trusted websites you will soon experience more and more organic traffic.
The rate of growth depends on the type of website, competition, type of content and other factors but as a rule of thumb six months is the minimum period until SEO for new websites will start to work.
SEO is the most reliable, repeatable, and consistent traffic source for the long-term growth of your website.
Just know that for new websites, it can take up to a year before you start seeing significant traffic numbers from Google.
Other traffic methods, like social media, community sites, quality traffic tool are essentially instant. If executed properly, you can get traffic immediately to your website. But, these are not repeatable strategies that you can do over and over again.
Therefore, the best traffic strategy is to focus on SEO. Publish really high-quality content, and build a lot of strong links.
If you do, eventually you’re going to see your rankings and traffic start to surge and grow month after month.