We don't automatically add on H1 tags to the homepage as it isn't a content page and the only place we could add it for consistency for all merchants would be the store's title set under preferences.
Admin → Online store
Title and meta description → Homepage title
This would then make your site title your H1.
It's possible to alter this, however we do think it's a missed opportunity as you can add a 'custom HTML' section to the homepage and add in your own H1 tag that targets the keywords you want to focus on, as well as adding a brief 'explainer' of what your store does on the homepage, so when people land on it they know exactly where they are.
The best way to directly add an H1 tag to the Home Page Template, is to use the 'custom HTML' section:
Online store → themes → customise
Choose "Add section"
Select "Custom HTML"
Add in the following code and alter the text between the two tags, to suit:
<h1>Your own custom h1, including any important keywords</h1>