You'll have to use PHP SESSION to remember it for the existing browser session.
But can you use PHP SESSION?
SESSION is stored on the server, but a temporary ID is stored on the client's PC.
So essentially, SESSION does the same thing as a cookie except it is removed when the
browser closes or the user "logs-off" (closes the session). A regular cookie can also
have that same feature ... dying when the browser closes.
$_COOKIE and $_SESSION both store something on the user's PC.
So my answer to you is no ... you cannot do what you wish to do.
... and what about pop-ups? what if those are suppressed?