How to check if the user can go back in browser history or not

Short answer: You can't.

Technically there is an accurate way, which would be checking the property:

history.previous

However, it won't work. The problem with this is that in most browsers this is considered a security violation and usually just returns undefined.

history.length

Is a property that others have suggested...
However, the length doesn't work completely because it doesn't indicate where in the history you are. Additionally, it doesn't always start at the same number. A browser not set to have a landing page, for example, starts at 0 while another browser that uses a landing page will start at 1.

Most of the time a link is added that calls:

history.back();

or

 history.go(-1);

and it's just expected that if you can't go back then clicking the link does nothing.

There is another way to check - check the referrer. The first page usually will have an empty referrer...

if (document.referrer == "") {
    window.close()
} else {
    history.back()
}