I think you are mistaken. There is no guarantee that a any solution will work for any given block. While the pool of possible answers is finite, it is so large that it can essentially be considered infinite for the purposes of considering an increase in statistical probability. If we consider the pool of potential hashes to be "finite" then we also have to consider that a resulting hash is not removed from the pool, since that same hash could be calculated again with a different set of data.
The next hash you calculate after incrementing the nonce is no more or less likely to result in a solution than then previous or the next hash.
I'm trying hard to follow you here. Your first statement insinuates that it is possible to build a block that has no solution whatsoever which I think is patently false. In the next statement you conflate a finite pool in which there is a correct answer with being so large as to be infinitely sized. If that is the case then it would possible and even likely that any given block could result in an infinite amount of time being required to solve it. Strangely enough, the network tends to solve blocks at roughly 10 minutes each with no happenstances where the network stalls out because it is going to take infinite years to solve this one. I will concede the point that hash collisions can be found in a sufficiently sized pool.