My team and I have recently purchased a Google Domain, but when trying to have the website it is connected to, it only gives us the options of website builders. We have a GitHub repository with all of our files that we want it to host, but again, only website builders. Can I make my Google Domain connect to a custom HTML page?
You can host your content on GitHub and serve them with GitHub Pages
You can have your Google Domains domain point to it.
https://help.github.com/articles/using-a-custom-domain-with-github-pages/
You'll need to add a CNAME file to your repo with your domain URL in it. Add it manually or follow the instructions here.
https://help.github.com/articles/adding-or-removing-a-custom-domain-for-your-github-pages-site/
You'll need to add some A records at the Google Domains control panel with the IP addresses of GitHub's servers (currently 192.30.252.153 and 192.30.252.154).