Haven't had a good facepalming in what feels like hours, so I'll bite
no, but there should be a way to win!
seems like you didnt care to think
Winning/losing a challenge in a game like this can only work in a couple of ways
a) if you fail you can retry, i. e. play parts of the game again
b) similarily you can get an additional challenge if you fail to get back on the "winning" path
c) failing or winning doesn't have much consequences except for one or two scenes and a slight change in some dialogue
d) failing leads to a game over (or, less likely, winning leads to an immediate "you win" happy ending)
But when, as here, major plot elements hinge on whether you win or lose, it has to be pre decided. If you had a real option, it would basically turn into two games with very different stories, meaning twice the story writing, twice the rendering, twice the amount of time needed for the same amount of content for the average player, also twice the disk space used.
That doesn't mean that a dev needs to include a "competition" like that, especially one that seems doable (though that adds to the suspense), it doesn't mean you have to be happy with the outcome, but facepalm everybody as much as you like, if
you "cared to think" about how plot driven games work you would have known from the beginning that winning isn't really a probable outcome. Even big studios can't really do it differently, the Mass Effect example mentioned above is pretty spot on (especially because that scene also was annoying af), you might want to read up on it since probably you are too young to remember.