Hugo is a static site builder.
This means that when you build your site, all previously existing files in the public folder are deleted.
One issue this creates is that the Google Search Console ownership verification file gets deleted as well, and without realizing it, your site becomes unverified.
To ensure that the Google Search Console verification file is output to the public folder along with your site when you run the hugo command (rather than uploading directly to S3), you just need to place the Google Search Console verification file in the static folder.