You won’t even know the cougar is there. If you doubt that, you must be the one in a million whose pet cat never comes up behind you without you knowing it.
I went on an Owl Outing in Southern California several years back. We went into the woods and were stalked by a mountain lion.
The adults thought it was pretty cool, but as we were accompanied by some children we thought it best to return to the main road and look for owls from there.
The cat was making plenty of noise in the underbrush. She was warning us away, not planning for a meal.