There are a few steps you should be taking...
1. Check on Google directly.
Type in "site:mystunningwebsite.com" into Google.
If nothing shows up, that means Google hasn't indexed your site
2. Verify & Submit Sitemap to Google search console.
Head to Google Search Console
Navigate to submit sitemap and enter "www.yourdomain.com/sitemap.xml"
They will notify you through email in <24hrs
PS: Shopify help also posted this short video