Hope, approached practically, works less like a feeling to wait for and more like a stance to adopt before tackling a genuine problem: an assumption, held provisionally, that a workable solution likely exists even if it has not been found yet, which changes how a person searches for it.
This stance affects behaviour directly: someone who assumes a solution is out there tends to keep testing options after an initial failure, while someone without that assumption tends to give up earlier, treating the first failed attempt as proof that the whole effort was misguided from the very start.
Adopting hope as a working stance does not guarantee a solution will be found, but it does keep the search going longer, which matters enormously in practice, since many genuine solutions are only discovered after several earlier attempts have already been tried and quietly discarded along the way. That willingness to keep looking, past an early setback, is arguably the most transferable part of the whole approach, useful well beyond whatever specific problem prompted it.