Hyde here from Shopify.
If you are transferring a third party domain over to Shopify, then you'll need to ensure you're following this guide. To ensure a smooth transfer you will need to keep the following considerations in mind:
You then need to make sure you've properly prepared your domain for transfer:
And then comes the actual transfer:
Before you receive an email from Shopify, you will likely need to receive an email from your previous domain provider - essentially confirming the release of your domain. If that hasn't happened, you will need to speak to your domain provider directly to find out if the domain has definitely been released.
I hope that helps, let me know if you have any other questions!
All the best, Hyde.