The easier route by far would be the server logs. The server knows which files it serves, and it doesn't care where the requests come from. Ask your ISP.
There is nothing special about index.html. It is just by convention the "root" file for a website which shows up when no specific file is requested, and it doesn't in itself do any tracking. (You used to get just a list of all files in the directory if index.html didn't exist, but providers tend to disable this by default these days).
A script embedded there wouldn't track any external requests for specific files. The idea would be to direct all traffic to the index file, but it doesn't prohibit anyone from requesting stuff directly. (Prohibiting could be done, though, of course).
I can only encourage you to read up a bit on html and basic web design, it's really not rocket science.