Only in islands can this hypothesis be supported. But islands are NOT continents, and that raises problems with the hypothesis. The most inconspicuous of which is timing.
In Australia, the gap between man setting foot on Australia and the extinction of Australia's megafauna was 17,000 years. Too long.
Man left Africa and set foot in Eurasia more or less than 50,000 years ago, yet the extinction of Eurasia's megafauna happened 10,000 years ago. Too long.
The oldest discovered American, "Eve", was discovered in a cave in Mexico's Yucatan Peninsula and dated to be 13,500 years old, 500 years older than the supposed time that man crossed Beringia. This could imply that man crossed Beringia at a far earlier date, yet the dating of the extinction of America's megafauna coincided with that in Eurasia. Too long.
There's also into consideration the Younger Dryas climate chaos phenomenon, which did coincide with the extinction of the 30 genera of Pleistocene megafauna, a handful of microfauna and plants, not to mention the Clovis culture itself.
If man was the cause of the extinction event, the gap between man setting foot in new lands and the megafaunal extinction would've been a few generations, not a few millennia.