Cole and another man went for a swim down the river on Saturday afternoon when a 16-foot-long crocodile snatched him and pulled him underwater.
Northern Territory police said about 15 campers witnessed the attack, though police have yet to find Cole's body.
While the Wilderness Retreat is a popular holiday destination, visitors are warned not to swim in the water.
'The Mary River is known worldwide to have the greatest saturation of adult saltwater crocodiles in the world. You don't swim in the Mary River,' a watch commander told reporters.
"I would never ever go in that water. Why that young man did I don't know," one Mary River camper told NT News.
Other witnesses said they heard gunshots as police searched in vain for Cole and the croc.