You can try to enable password protection, Shopify will add all URLs in private mode, Google cannot crawl your website:
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From your Shopify admin, you go to Online Store > Preferences.
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Scroll to the Password protection area, and check Enable password.
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In Password, enter the password that you’ll give to the customers who you want to be able to access your online store. Don’t use the same password that you use to log into your admin.
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In Message for your visitors, enter the message that you want to show on the password page. If you don’t want to show a message, then leave this field blank.
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Click Save.