Other answers already describe how you can go fullscreen in a more or less browser-independent way.
However, problem of needing user interaction remains.
You cannot force your webpage to display in fullscreen mode for security reasons.
User interaction is required for that.
Also, browser leaves fullscreen mode whenever user goes to another page, even on the same website, and (s)he will have to perform some "user interaction" on every page to go back into fullscreen mode.
This is the reason why your website has to be a single page if you want it to be fullscreen.
That is what I suggest:
Use a single splash page that has a hidden iFrame on it.
Whenever user clicks anywhere or presses any key, just set this iFrame to be fullscreen and show it. When you receive an event on leaving fullscreen mode, hide iFrame again to show splash.
Links open in the same frame by default, so you will stay in fullscreen mode until user explicitly leaves it or some links opens in a new tab.
Here is an example that works in Chrome:
(See it in action. Use other answers to make it browser-independent.)
<html>
<head>
<script language="jscript">
function goFullscreen() {
// Must be called as a result of user interaction to work
mf = document.getElementById("main_frame");
mf.webkitRequestFullscreen();
mf.style.display="";
}
function fullscreenChanged() {
if (document.webkitFullscreenElement == null) {
mf = document.getElementById("main_frame");
mf.style.display="none";
}
}
document.onwebkitfullscreenchange = fullscreenChanged;
document.documentElement.onclick = goFullscreen;
document.onkeydown = goFullscreen;
</script>
</head>
<body style="margin:0">
<H1>Click anywhere or press any key to browse <u>Python documentation</u> in fullscreen.</H1>
<iframe id="main_frame" src="https://docs.python.org" style="width:100%;height:100%;border:none;display:none"></iframe>
</body>
</html>
Note, however, that websites often disallow embedding, e.g. being displayed inside an iframe. The example initially used W3Schools website instead of Python docs, but they set 'X-Frame-Options' header to 'sameorigin' (disallow cross-site embedding) and it stopped working.
P.S. I like the idea of simulating full-blown OS in browser, and it's even better in fullscreen! :) Change your OS!
Also, I am not a web developer. Just thought this question would be interesting to investigate.