Thank you for reaching out with your question. The "coming soon" message is likely the password page, which is enabled by default when you begin your trial and can be disabled once you have chosen a Shopify plan. The option to disable the password page appears in Online Store > Preferences in the Shopify admin.
In terms of the domain, is this a domain you purchased directly via Shopify or was it through a third party? Does a message appear next to the domain, such as "SSL pending" or "SSL failed"? If you could also tell me the name of the domain in question I'd be happy to take a closer look at this for you.
Victor | Shopify Social Care