It was a bit more complex than the Shopify Help Centre would suggest, which is why I will describe it here:
- I first had to authenticate my domain
- I then had to upload the sitemap to Google Search Console (as described in the Shopify blog)
- In the Search Console I had to go to "URL inspection"
- I had to provide my URL
- I had to request indexing
Now that it's done, I will look into creating more blog content to start driving more organic traffic to the site.