Question

Why do amphibians and frogs seem to appear suddenly after the rain?

Answer 1

Because that's when they are safest from their predators. The predators are still hiding and waiting out the rain.

Answer 2

Since their natural habitat is water, it becomes flooded when it rains. In order to avoid death, they appear almost anywhere with water bc it's similar to what their used to. After the flooding decreases, they go back to their original habitat.