I would suggest using this app https://apps.shopify.com/gobot-1 you can create pop-up quiz, give instant results, and there is one option to collect customer emails as well.
It's free for 1st 5,000 engagement so I guess that's all you need to test it out.
Let me know if that's helpful for you.
If you aren't looking for a popup, you can utilize Jebbit.
Can do the functionality you are looking for but can be embedded on your site, or, can be used across email/social/paid ads/etc too.
Free plan that you can test as well!
Please let me know if you have any questions or we also have a great support team to help.
I think it's possible to do it even with the help of Shopify, you can search related forums as well. It's strange this complicated question hasn't been discussed here. I would definitely help you if I know any information connected with it. But I can suggest you something interesting. What quizzes are you interested in exactly? It's a big pity you haven't mentioned your preferences. I love to search for different entertaining quizzes and then play them daily. I am sure you will be astonished in a very pleasant way after visiting https://quizlagoon.com/quiz/harry-potter-house-quiz-ravenclaw/ this source and solving the quiz displayed there. And I won't be surprised if you find a new job after it, ha-ha...