Hi, @1LT !
My name is Lilith, I’m on the Social Care team at Shopify.
You’re totally correct that uploading an HTML file isn’t the best way to do it with a Shopify hosted site.
The easiest way to do this is to either edit your domain DNS settings or add those meta tags that Google provides to your theme code. Don’t do both, just one is enough.
With any of the methods you have available, they will take anywhere from an immediate update to 72 hours to update online. This is normal and common for anyone setting up GSuite anywhere.
I highly suggest the DNS settings method as this is less likely to break the site if a small error is made. I’ve got some screenshots below on how to do this in Shopify if you bought your Domain with us directly.
1. In your Shopify Admin go to Online Store > Domains.
2. Click on Manage next to your domain as shown below.
3. Click on DNS Settings as shown below.
4. Click on the Add a custom record menu button as shown below.
5. Follow your custom outlined “generic” instructions from Google Suite to help you fill in the fields for the TXT record(s) you need to add from the Add custom record menu. Make sure you’re logged into your GSuite admin account when accessing that Google page. There may be specific record values you need to generate in order to copy and paste. The instructions are pretty great on there with the visual steps as well for your GSuite account.
6. Don’t forget to add those GSuite MX Records into your domain DNS settings to use your branded email as well if you wish to do that. I recommend it so that you can improve your brand identity.
7. Save your DNS settings.
I’ve included embedded links to Google’s step by step pages as well to help you with the correct instructions.
Let me know how you do with the information above! I’m happy to answer any questions you think of as you work on your business.