The simplest solution is to make a static website of your dynamic one using wget, and then publish that. I did this e.g. for Wordpress sites, works really well and is very reliable. The process can be triggered via a cron script or manually (I wrote a small Wordpress plugin for it). No special hardware, infrastructure or cloud services required. Just make sure all resources are reachable via a link (so wget can find them) or manually point it at a list of otherwise unreachable files (e.g. using a sitemap or .txt file).
The advantage is that you can still use your existing CMS, so your staff won't need to learn a new system, and you also don't need any third-party cloud services.
Actually, if your CMS is properly configured (e.g. correct cache headers) you can also simply put it behind a CDN like Cloudflare, which will handle the caching and scaling for you.