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I personally don't subscribe to a "young Earth" theory, and I suspect hominids (albeit, not humans) existed prior to Adam and Eve in Eden. My church teaches a recreation at the time of Adam and Eve following an unspecified event (possibly a Satanic rebellion) that rendered Earth "chaotic and void" (Genesis 1:2), which follows from several key scriptures as well as the nigh indisputable fact (assuming constancy of physical laws) that the Earth is several billion years old. Hence I can only refer to young-Earth theories by proxy, having no detailed knowledge of them.Yes - there's some controversy, but it hasn't been proven to be wrong by orders of magnitude that might suggest something determined to be 12,000 years old is actually only 2000 years old.
The issues with it are typically more when looking at things older than 20,000 years.
So the 12,000 year old skull is surely well within a confidence level of >95% (guessing here) regarding age.
Having said this, what little I have read in that domain points out that radiocarbon dating is beholden to assumptions about levels of atmospheric 14 carbon, Earth's magnetosphere, background radiation, the media in which samples are excavated, and other variables, and contends that huge errors are indeed very possible (likely, even) when these assumptions are violated, especially for samples older than 3,500-4,500 years where the concentration of residual carbon 14 isotopes is extremely small.
If you search on the subject, you'll find dueling claims, debunkings, debunkings of debunkings, etc. Enough to keep you occupied for a lifetime, I suspect.