I will point out that although carbon dating really doesn't work beyond a certain distance into the past--50,000-60,000 years old seems to be the limit--we can nevertheless confirm that carbon dating does work for the few thousand years of recorded human history--does carbon dating give an age of 1500 years for a document we know was written in 500 C.E. ("500 C.E." = "500 common era" = "A.D. 500" = "anno domini 500")? If we know a monument was built in 2000 B.C.,E., does carbon dating give an age of about 4020 years? We can test it against things whose ages we already know. Turns out, it works well within its range of applicability, which increases our confidence in radiometric dating generally.
I will also note that that's a special case of dating objects in more than one way--ways neither of which depends on the other--and, when the two methods give comparable ages, it increases our confidence in each of them, because it can't be said that a flaw with one method is affecting the other (as they're independent). That's why I sometimes bring up the case of ancient coral. Trees grow rings, one ring for each year, so you can tell how old the tree is by counting the rings (and can also test carbon-dating against the tree-ring count, which works nicely). Coral grows bands (but daily), and in such a way that it's possible to tell how many days there were in a year when the coral grew. Now, the number of days in a year is not constant. Physicists know that the Earth's rotation is slowing due to tidal forces with the Moon; the Moon is growing more distant from the Earth, and the Earth's rotation is slowing (these conserves angular momentum). Coral having 420 bands grew, if physicists are doing their calculations correctly, in the range of 430 million years ago, because that's when the Earth's rotation was sufficiently much faster for there to have been 420 days in a year. And radiometric dating gives a comparable age. This reinforces our confidence in both methods of dating--and helps us learn about the past. (You can read about this here: https://www.theatlantic.com/science/archive/2016/02/fossilized-coral-calendar-changes-leap-day/471180/ )
It's not as simple as I'm making it sound--scientists are aware of various complications in radiometric dating that have to be taken into account if you're not to get wildly wrong answers--but that's the point: scientists are aware of them. Might there be other complications yet to be discovered? Sure. But that's why you try to use more than one method of dating wherever you can. (I seem to remember there being a third, having to do with mineral sedimentation, in the case of the coral). That way, you gain confidence in each of them.
I think that underlying much of the disagreement in various threads are a few simmering fundamental questions. "How can we gain knowledge about the past" seems to be one of them.
Obviously, we can't see into the past--we can't just look and see what's true about the past. For recorded human history, we can at least look at documents written by human beings--at least, the documents we've found. But once we get past recorded human history, how do we gain knowledge about the past?