The stupid-simplest solution I ever saw for this was all the way back in the Slashdot era, where people would filter on refer headers and redirect all traffic from news sites to the Google cache version of their page.

That works great for static pages. Hugo and Jekyll are basically precompiling static pages.

For a more dynamic site? I know some people who do special handling for bot and spider traffic. The bots get not exactly static content but much less dynamic content. I could see rerouting all traffic, especially for everyone without session cookies, to that version during a big spike.

Those solutions behave a little bit like the eventual consistency you see on very large websites, where values are approximated or cached with a very short TTL.

As others have commented, the simplest way to get that on a small site is to pony up money for a CDN. Maybe not the cheapest, but certainly the simplest.