This question is mostly just out of curiosity at what's possible. I'm interested to know any ideas at all.
If I'm on a website, is it possible to make a keyboard shortcut for clicking a button on that site? For example, if I'm on google.com, is it possible to write a script somewhere on my own system that will detect that I'm on google.com and make it so that if I press ctrl-g while that site is in focus, it will click Google Search?
If you know for sure that this isn't possible and have an explanation for why, I'd be interested to know that too.