I purchased a domain through Shopify about six days ago. How long will it take before people can goggle search and have it show up?
Congratulations on opening a Shopify Store. Have you already linked your domain/website to Google Search Console?
Google needs to index your page first to know that your website exits. I would recommend to learn about indexing your page and a bit more about Google Search Console to get started on this.
I am there to help, so do let me know if you run into any blocker.