How to set up GitHub Pages to look for index.html in a different location?

No.

You would need to change the site source to change the directory where Jekyll will read files, but this is a configuration setting that you cannot change in GitHub Pages:

https://help.github.com/articles/configuring-jekyll/#configuration-settings-you-cannot-change

You can, however, change the source to the docs folder in the settings of your GitHub repository.

See https://stackoverflow.com/a/41197820/2102854.

You can try this: create a dummy index.html file at the root, and insert this line of code and give it the right path.

index.html

<meta http-equiv="refresh" content="0; url=https://yourname.github.io/myapplication/frontend/public/index.html" />