1. simulate a world with very basic "physical" rules (so it is free from human bias)
2. let the simulation run until organisms exist
3. let it run longer so the organisms develop language
4. now see if the organisms talk about things like "consciousness" and "why are we here"
The nice thing is that we don't have to do the experiment to think about what it means if 4 happens or not.
I'm not sure I've ever met anyone I would assume has not considered the basic questions of our existence. Unless they were severely mentally disabled, or something like that.
For a more public measure I suppose you could look at religion, which seems to be a fundamental attempt at answering those questions. Most people are religious or have some kind of religious belief.
You said it yourself, you would assume they question it, meaning you are not certain. This topic is always very much tabu, and the system is built to classify automatically every One that question it as weird and not normal. Religion should be banned, as is misleading and idealogically harm people by brainwashing them. I live in Europe and was in Canada (Waterloo) for a bit. The difference of social opinion if you follow or not religion is huge, I was shocked. Growing up in Italy I can confirm that even Italy is not so brainwashed by it.
This question is the subject of so many poems, so many pieces of literature, so many movies, that you're forced to confront it multiple times in school, and you're forced by your very existence to confront it once you hit certain levels of mental development. You're forced to confront it many times in your life - perhaps first when you gain a theory of mind (before age 10), again when you first truly realize you will die, again when someone very close to you dies, when you propose/marry (if you do), when you have your first child (if you do), when you get a cancer diagnosis (if you do), when you consider taking your own life (if you do)... all of these common life events force you to confront it deeply.
Most people make peace with it in some form, and most realize that questioning it daily does not make a difference, you simply have to either accept an answer (whether that's "god", or "for no reason", or "I'm not sure yet, I need to check back in after I get older"), or decide that there is no simple answer, and they have to live with that.