"Caveman" is a general name used to encompass several groups of fossils including Neanderthals, Cro-Magnons, Homo-Erectus, Denisovans, and Homo floresiensis (also known as "hobbits"). Scientists have to make assumptions as to their characteristics based on fossils, bones, and artifacts found near them, so there are a lot of "maybes" and "possibly" associated with any discussion. Another problem is that secular scientists and Young Earth Christian scientists see the evidence through two very different worldviews. Secular scientists believe humans evolved through a progression of creatures from ape to modern man. Young-earth creationists believe God created everything — ape and man — within the six days of creation. To the former, cavemen are a step to us; to the creationist, they are us.
Does the Bible mention prehistoric men such as cavemen or Neanderthals?
Neanderthal is the name given to a type of fossil found mostly in Europe, with a few outliers in Central Asia and across Africa. From their bones, we know they had a pronounced brow, a large cranial cavity, and a short, stocky frame. Their remains are mostly found in caves (whether because most of them lived in caves or because caves are particularly suited for preserving bone, we don't know), giving them the nickname "cavemen." In secular science, there is debate as to where they belong. Some call them another species in the genus Homo and claim they are either an evolutionary step between apes and humans or a dead-end offshoot of advanced apes. Others, including Christian scientists, consider them to be another ethnicity of Homo sapiens (Homo sapien neanderthalensis — Humans, by contrast, are scientifically classified as Homo sapien sapien).
Neanderthals have a storied past in Christian culture. For a while, they were vehemently denied. Then they were postulated to have been humans afflicted with a bone disease. Now they're generally accepted as another ethnicity of human. In fact, it may be that young-earth creationists were quicker to accept Neanderthals as human than evolutionists. Today, Christian scientists agree that they were a tribe of people who dispersed after Babel, but there is discussion about why Neanderthals have such a distinctive appearance. Some hold to micro-evolutionary changes caused by limited sunlight, poor diet, and/or disease (including rickets, arthritis, and syphilis). Others speculate the pronounced forehead and large brain capacity were related to their very long lives. It also isn't known why Neanderthals disappeared. They may have interbred with other tribes, or they may not have been able to adapt to the post-Flood Ice Age and subsequent thaw.
Cro-Magnon are thought, by evolutionists, to be a step behind Neanderthals, although their skeletal structure is mostly like ours, with a few nods to Neanderthals such as a stocky build and a larger head. In reality, the evidence could also say that modern-like humans, Cro-Magnon, and Neanderthals lived at the same time and interbred to derive such variety.
Denisovans is another group, identified by a chip of a finger bone found in the Denisova Cave in Siberia. A DNA analysis was done which found very few differences between the girl to which the bone belonged and Neanderthals. Creation scientists see no reason to believe "Denisova" is anything than another tribe of human; their DNA markers indicate they migrated east, and contributed to the genetic makeup of people in India and Australia.
Homo floresiensis, also nicknamed "hobbits," are unique because of their size. They stood about three feet tall, with proportionately small heads. Initially, some thought they might have microcephaly, which doesn't allow the brain to fully form, but this has since been refuted. On the basis of their skull size alone, evolutionary scientists claimed they were another dead-end stub of human evolution, but creationists believe they were just small people. Their fossils are only found on an island in Indonesia; such a restricted area could have resulted in the incest and micro-evolution that resulted in their size.
The Bible gives no mention of a tribe or tribes that resemble cavemen, but the Bible doesn't dwell on physical appearance too much, anyway, unless the person was unusually tall. Neanderthals might have been at the Tower of Babel, and they might have left earlier. Most likely, Denisovans were just a tribe that lived north of the Neanderthals and headed east. We don't know why "cavemen" went extinct or what place they had in history. We don't know why they looked like they did. We don't know if they had long lifespans or short. Or if they were diseased. Or if they disappeared because they mated into other human tribes.
It's just interesting to note that the more scientists study the remains of "cavemen," the more they seem like us. They may look different when illustrators give them dark, gorilla-like skin and wild hair, but it doesn't mean they were different. Noah's family had the genes to give us everything from the pale skin of Scandinavia to the short height of Pygmies to the deep brow of Australian Aborigines. There's no reason to think there weren't also other extreme body shapes that integrated into the human race.
Do Genesis 1 and 2 record two different creation accounts?
What is the origin of the races of humanity?
Why did God create humanity?
What does it mean that humanity is created in the image of God?
How old is the Earth?
Truth about Creation