Thank you for reaching out to the forums for help with your online store checkout! Congratulations on launching your store, although I can definitely understand your concern if your checkout isn't showing eligible shipping rates.
A few things to check and some steps you can apply in the interim to allow customers to check out. In your store admin go to Settings > Shipping to check these options:
From the Products page in your admin, select all products then the "Edit Products" button to open the bulk editor. This will allow you to quickly check all your products for any inventory issues. You can add columns to the bulk editor to quickly see these different options:
I wanted to throw out some suggestions to help you with this as quick as I could! If this doesn't resolve the issue or you aren't sure where to check for these options please reach out to our live support for faster troubleshooting help. To contact our live support please follow this link: Shopify Help Center - Contact Support, sign into your store account, search for your issue and use the contact support button at the bottom of the search results to see all our live support options.
Let me know if you are able to get this resolved!