thousands of times a second

Modify your Nginx (or whatever web server you use) config to rate limit requests to dynamic pages, and cache them. For Nginx, you'd use either fastcgi_cache or proxy_cache depending on how the site is configured. Even if the pages change a lot, a cache with a short TTL (say 1 minute) can still help reduce load quite a bit while not letting them get too outdated.

Static content (and cached content) shouldn't cause issues even if requested thousands of times per second. Following best practices like pre-compressing content using gzip, Brotli, and zstd helps a lot, too :)

Of course, this advice is just for "unintentional" DDoS attacks, not intentionally malicious ones. Those are often much larger and need different protection - often some protection on the network or load balancer before it even hits the server.