If you’re using PHP, you can parse a /blog folder and generate the blog index that way. You could do it on the fly (low traffic) or run it every so often via cron to generate the page. There are lots of options if you’re using PHP.
I was thinking of doing something similar but for generating WebP images. If I did this method for the blog index, is it just a matter of checking the last modified on the file, grabbing the information and then loading it into a HTML static include?
You could do that, or you could simplify it and just run it every so often to regenerate everything. Unless you have tons of files (or unless the script requires a lot of resources, e.g. image processing), caching probably isn’t a priority.