If a flying creature with no swim speed ends up in water, can it fly out?

Assuming there is no magic holding it aloft and it doesn’t have the ability to hover, when a flying creature is knocked prone, it falls.

What happens if the creature was flying over a body of water? Can it effectively use its movement to "stand up" on its next turn and resume flying, or does it end up like that video of the bald eagle swimming, where its feathers are too wet and it can’t reasonably get enough lift to take off again?

Ducks can take off from water, but I would argue that ducks have a swim speed.