I think it's an interesting question and one I've discussed with people before in slightly different way.
Saw on the news earlier this week that there's a local play happening that retells the birth of Jesus with the story set in present-day Brooklyn. That led me to thinking about how a teen girl who showed up pregnant yet insisted she was a virgin, impregnated by God and destined to bring forth a savior would be received. Yall better hope your Lord doesn't try to come back the same way he got here because no one would believe that story.

I digress... It got me to thinking about the story of Jesus' conception. People of the Bible did all kinds of things because God said so and people today would do so too. I don't think "choice" would've even factored in. I don't think Abraham wanted to kill Isaac but he did choose to do so... he chose to obey God and if a consequence of that was to kill his son, then so be it. He trusted that God knew things he did not. Mary probably also believed as such and it never occurred to her seriously to choose otherwise, if choice was even a consideration.

I'm no Christian but I would think that faith should withstand questioning, curiosity and criticism. Indeed, it should be viewed as an opportunity. A lot of Christian folk get super defensive about it though, as though even calling the question is an affront. We live in a majority Christian country and people of other faiths/no faith are constantly bombarded with pro-Christian imagery, messaging, customs, etc. I think we can deal with a few hypothetical, imaginative questions that invite people to think. Even as we wrap presents and listen to Mariah Carey's Christmas album on endless, godforsaken loop.