Think of your PhD not as as finding solutions for a specific problem you have in mind, think of it as working in a specific area of research. Like with a startup, you usually have to pivot your research because things don't work out as imagined, and other directions turn out to be more fruitful.

With that perspective, it doesn't matter much on what specific problem you start your research. Instead, find out which research groups are doing amazing work in the area you would like to work. And apply there.

To identify these groups, read a lot of papers in your favorite research area.

That is one of the subtler points of the PhD - you can't just do what you want, and certainly not at first. The ideal is to find a professor who has a project that aligns with your own interests. If your hope is to find a professor who will back a wholly new project you thought up, that's kinda hard to do during a Master's.