There are two schools of thought on "cavemen."So what does that infer about numerous cavemen and inferior species of "men" who existed before Adam, many thousands of years ago, even before the last ice age?
One is as you suggest, that creatures like men existed between Gen 1:1 and 1:2.
The other is that the fossils of cavemen aren't nearly as old as science thinks they are, that they were small groups of people who inbred to the extent that they were malformed.
I'm not sure which is true, but I do believe that Adam was created ~6000 years ago and every human on the planet that has existed since then is descended from him.