Did you try the Google search console? You can submit, verify your website and sitemap. It may take some time after you do this. You will be able to check the URL, view the tested page etc.
Here is the link that shows how to get on google if you want to try.
To appear in search results though, Google has to first find your website content. You can submit your store's sitemap in Google Search Console.
I suggest you install flare by Mansion Ecommerce. Instead of waiting for Google and Bing to find website pages, flare pro-actively, and verifiably push site updates to major search engines daily.
Focus on creating content relevant to your customers, brand, and business. Let flare worry about informing Google, Bing, and many major search engines of your awesome content.
Hope this helps,
The best option is that you can try Google Search Console where you can submit sitemap and register your website and also helps you to monitor, maintain and troubleshoot your website's presence in Google Search result pages.
Another simple solution is (For a Physical store) is to add your business to Google Map:
1) Go to Google My Business after that click on Get on Google
2) Enter your business information in the search box
3) Select or add your business in the menu bar
4) Verify your business which will take 1-2 weeks for a postcard to arrive with a verification pin
5) Confirm your business by setting up a Google+ page which is the first and foremost step in local search optimization and should be the highest priority these days for all businesses online.
Please try Google Search Console and after verification submit your live site and it's sitemap.