Get current time in JavaScript when the browser retrieves a cached html page

I’m having a html-page which is cachable. At the end of the page, I put:

<script>
    console.log(Date.now());  
</script>

I load the page: The console shows 1695306780514.
I follow a link on that page.
I press the back-button of the browser.

My assumption was that I now get the current datetime, a little bit later than the previous one.

But:

• Chrome (on Windows) shows the same 1695306780514, not the current datetime in console.
• Firefox (on Windows) shows just nothing in console.

I even tried

$(document).ready(function() {
    console.log(Date.now());
});   

or

var showDate = function(){
    console.log(Date.now());
};
window.setTimeout(showDate, 1000);

but the effect is exactly the same.

How can I make sure the javascript is executed again and uses the correct datetime?