There is most definitely a pre-existing WP theme or plugins out there for creating a quiz/trivia site. You could also build your own custom theme to do the job.
Of course wpbeginner has a list of plugins, here.
Initial thoughts are a custom “notecard” post type with custom fields for things like category, correct answer, incorrect answer 1, 2, 3, etc.
Have a page template with buttons that randomly fetches one at a time.
Where my php skills break down is handling the logic for gameover, keeping score, etc.
I like the idea of being able to leverage WP for user management, admin editor.
In looking at what’s out there some cool features I see include:
Templates, leaderboards, certificates, quiz branching, drag and drop, countdown timer, force user to take an action to view results, hints, comment/explanation boxes, multiple question types (true/false, fill-in-the-blank)