Sometime Google drop sites (Google Shake) so if you noticed this you have to login to your Google webmaster tools dashboard and choose:
Crawl > Fetch as Google
Check you website Sitemaps (if there is an errors). and resubmit it once again.
Check if there is a blocked content preventing your website from appearing in SE, like robots.txt file, htaccess file or other files can prevent your website from appearing in SE.
Your website is now being shown in Google search again.
Although only your front page - I'm sure the rest of the pages on your site will get indexed with time.
The best SEO tip I can give you is to not over-analyze the search results this early and just focus on building your store and making it as good as possible instead.
Keep adding products and build backlinks to your site and in time you'll start to have some organic traffic starting to trickle in. Good luck with your future marketing efforts and your new store!
Make your site showing up on google search is a long-term and really-take-time process. You should have some knowledge about Shopify SEO optimization. I just came across this article and it perfectly fits your concern:
Very basic but good technique to start! Hope it helps ;)