WordPress Super Cache plugin  is “A very fast caching engine for WordPress that produces static html files”. If you need to start any kind of session with your wp-super-cache plugin, the easiest and simplest way is to add your session data to plugins/wp-super-cache/wp-cache-phase1.php file.

In my situation, I need to add Yoast Gravity Referer session data to my website. So I have added below session values at the top of plugins/wp-super-cache/wp-cache-phase1.php file.

<?php
session_start();
$_SESSION['gf_yst_referer'][] = $_SERVER['HTTP_REFERER'];
$_SESSION['gf_yst_pages'][] = "http://".$_SERVER['SERVER_NAME'].$_SERVER['REQUEST_URI'];

By this way you can keep your unique session values for every visitor, because wp super cache serves static html files but keeps running wp-cache-phase1.php file for all requests.