No, but I stipulated unarmed or environment-armed.
“The chimp-like ancestor was like a power athlete,” said Dan Lieberman, a biological anthropologist at Harvard University. “Much stronger and faster than humans, but they had no endurance.”
Maybe he plucked it fresh from a revolver tree, smartypants.
I’m an American. Small arms are part of my environment
I remember that show; it wasn’t the audience who won – trust me on that one. 
Most likely the “caveman”; he’s going to have a lifetime of experience at wilderness survival and fighting, not just what little training or experience the astronaut has. Most likely the astronaut never even sees the “caveman” and dies in an ambush.
This is like asking what would win, a shark or a lion. The answer? Depends where.
On ice or grass?
Simply not true. Late Paleolithic Eurasians (the best “caveman” candidate) had an average male height of a little over 5’9", with well over 6-foot-tall individuals around. “Cro-Magnons were robustly built and powerful. The body was generally heavy and solid with a strong musculature.” Cite
North European Stone Age people typically exhibit high bone density and mass, with prominent muscle attachment points. Cite
Plenty of evidence of cavemen experiencing violent encounters, as well: concentrated blunt force trauma in skulls, parrying fractures in lower arms, projectile points embedded in spines etc. These people were used to fighting and most definitely had tactical skills and close combat experience. Bigger brains than us, too.
A caveman would almost literally eat an unarmed astronaut alive.
Yeah, an adult healthy caveman will probably be in vastly better physical condition even than an astronaut, especially for fighting. Astronaut physical training is about all around health and stamina, cavemen tend to have been “trained” by becoming physically adapted to a world in which you need to have stamina and physically explosive strength, ready at a moment’s notice. The cavemen who fail to develop both of those, do not become adult cavemen.
Even the “gathering” part of hunter-gathering would break most modern men down into crying, puddled masses of quivering humanity. I’ve read accounts of missionaries and anthropologists who have tried to keep up with the native peoples of the Amazon just going about their day to day lives and the results have been very poor for the first worlders.
If you want to put a caveman in a competition, that requires highly specific adaptive training like modern Olympic-level weight lifting, sprinting, swimming then yes, the caveman will get smoked. He’s not adapted to those things. But beating someone literally to death? That’s exactly his game, and an average adult caveman has spent decades doing nothing but live in a world in which he has a threat of death from his environment every single day. I would’t want to scrape with one unless I had a gun and a clear line of sight.
Napoleon said that fighting the British was like an elephant fighting a whale, the point being that his armies were strong on land battles, while the British navy were strong on the seas.
The whale won.
The whale was part of a coalition of animals and weather that won.