It can take up to a few weeks for a new website or store to appear in Google - as it takes time for Google to become aware of you, and then crawl and subsequently index. That said, there are ways to expedite the process, and we recommend the following:

Use the Search Console to submit your URL to Google

Link to your website or store from existing sites on the internet - whether that be your twitter, Facebook, your blog or anywhere else, which ideally already has some popular. A lot more tips are generally covered in the 'How do I drive traffic' article. 

Submit your Sitemap to Google - as explained in our Sitemap article