There are enough anomalies in dating methods to question them. At the time scales we are looking at, we have little or no knowledge of the actual circumstances of the environment at the time. Every kind of dating methodology that goes outside of human history relies on very specific assumptions. If we are wrong about any of those assumption then our dating methodologies become unreliable.
Even inside human history, we make various guesses about when various events take place. The extant records that we use to date any particular item or event lead us, in many cases, to a best guess. How accurate this guess is - well, who really knows.
Quite often, there is conflict over when or even if certain events have occurred in the past. This is the nature of the lack of easily obtained records of the past. Even when there is extent documentation available, there is still conflict.
I take all the prognostications of dates in the far past as a guess, since we don't really know.
> However, we humans are also incredibly good at finding clever, credible ways of inferring things from indirect clues.
We are not as clever or even credible in a lot of what we do as humans. We are far too biased and political even in the fields of science and technology. That is just a part of our nature. If you looked at all the controversies over the last, what, 300 years, or we could look back over the last 2500 years and we'll see this rear its head many, many times.
I have stated the position that we should not be concerned that we are certain, but put in the efforts to keep investigating all areas for insight and further knowledge. It really doesn't matter if our models are incomplete and wrong as long as we keep moving forward. It's when we are certain that we lose the ability to move forward. In many areas in science (even in technology) we have become "certain" that our theories and models are correct. This is a problem and we need to address this.