Basically, you're asking how long it would take you to get out of the Google Sandbox.
If your site is fairly new and produces content, it can take a while for Google to rank your pages to the point that you're getting organic traffic.
Sure, you will get a few bites, but it's not going to be significant.
You should focus more on creating content that targets the needs of the people you want to reach.
There are two ways to do this.
You can do keyword research based on what you think your audience would be interested in.
Or you can do what I do: look at your competitors, reverse engineer them, and find topics their content triggers, but easier to rank.
Filling out your websites with this type of content will make you bounce out of the Google Sandbox sooner than later.