Break difficult things into pieces small enough to argue with individually.

Something described as one large impossibility cannot be argued with, because there is no handle on it. Broken into pieces, each piece can be examined, and most will turn out to be either doable or based on an assumption that does not survive inspection. The breaking down is what creates something you can actually engage with.

Take the thing you have been calling impossible and split it into six parts. Go through each and ask whether it is genuinely fixed or only assumed. Usually at least two give way immediately, and the whole shape of the problem changes.