Strengthening the arch is definitely the way to go. Hiking is probably the ultimate way to do it, but walking is good too.

I've had plantar fascitis a couple of times before (decade apart) and I've found that it can be resolved within 3 weeks.

The trick that worked for me is to regularly stretch the foot / arch after a few minutes into a walk when the foot is warmed up. If I do that consistently near the beginning of every walk, the pain quickly fades away and the problem resolves itself.

I think hiking over technical-ish terrain, like stumbling over tree roots and rocks that hit the arch would provide the same action of stretching of the bottom of the feet.