If you are transferring the third-party domain to Shopify, it can take up to 20 days for your domain to be transferred. After it's transferred, you receive a confirmation email from Shopify, and you can access your domain settings on the Domains page in your Shopify admin.
The best next step for you now is to contact the Shopify Support team directly and have them check it for you.
You could refer to this link, log in to your store account then type in a topic in the search bar, for example, "transfer domain confirmation email" and select Search. On the following page, scroll down to Get Support and click Continue and you'll be presented with options to contact their Support via chat, email, or schedule a call-back.
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