If your website is new and your domain is under 6 months old then your website will be put into Google Sandbox to let it mature.
Once your domain and website ages to 6 months then your website should be taken out of the Google Sandbox and then you should start seeing your content ranking in Google search after 6 months.
It can take longer though for your websites content to start ranking higher in the search results on Google and some content can take a few years before it ranks on the first page of Google's search results.
Be sure to constantly add new blog content so Google will see your website as active and fresh and will keep your rankings up.
So after 6 month you should start seeing a little search traffic from Google search to your website or blog.
It can take a few years to start seeing huge traffic though since SEO and ranking is a long term process and your rankings will improve overtime.