the best solution for this is using livewire, or js countdown, with the quiz duration, and once that is reached redirect the user, and you need to create a new column in your database and name it open_until and store the quiz time
for example = now + 15 minutes.
and here is a JS code that may be helpful for you
var countDownDate = new Date("Jul 25, 2021 16:37:52").getTime();
var myfunc = setInterval(function() {
var now = new Date().getTime();
var timeleft = countDownDate - now;
var days = Math.floor(timeleft / (1000 * 60 * 60 * 24));
var hours = Math.floor((timeleft % (1000 * 60 * 60 * 24)) / (1000 * 60 * 60));
var minutes = Math.floor((timeleft % (1000 * 60 * 60)) / (1000 * 60));
var seconds = Math.floor((timeleft % (1000 * 60)) / 1000);
}, 1000)
``