"...recent things are sometimes dated as ancient."

If you understand what radio-carbon dating is, and how it works, you cannot rationally go on to believe that false or faked dating of any significant magnitude can occur.
The "Iceman" found in Austria lived about 5300 years ago, and he was nowhere near the Biblical lands.

Woolley Mammoths have been found in ice that were dated to 35,000 years ago. This was not faked, nor was it bad science. The decay of certain carbon atoms simply happens at a fixed rate, and if certain conditions are met, can be dated very accurately. To disagree with this 'because' you already have the 'authority' of counting vaguely described generations in Genesis is simply closing the mind to sound evidence.

You are free to assert that "God started it and planned it this way", but you cannot rationally assert that "it has all happened in only 6000 years or so."