It could take a few weeks for Google to update the meta title/description after the website is live. To streamline the process make sure to add the site to Google Search Console. https://search.google.com/search-console/about
Double check that the homepage title and meta descriptions are properly added. You can check by going to Online store > Preferences > Title and Meta description section.
I appreciate the context that you have shared with us as that is super helpful! Looking into this, the reason that you may not be able to find your online store on Google’s search results is because the store is new. Search engines regularly index new sites and if your site is new, it might not have been indexed yet. With that being said, you can find and submit your sitemap to prompt Google and various search engines to index the online store.