While I couldn’t make a working solution for a static site (i’m sure there’s a way and you can email support@glitch.com to figure it out), I did find this very interesting forum post on how to convert your static site to a server project (and get the custom 404 working).
There are some downsides such as no more 24/7 uptime but it’s the only solution I could find. I hope this helps. Let me know if you figure something else out, I’d love to hear it!