One way might be to find the oldest writing samples. If a civilization is said to have existed 250,000 years ago, but the earliest writing is only 5,000 years old, then I would have to doubt the first number.
As far as I know, no significant culture in Mexico pre-dates the Olmec culture, and that dates back to about 2500 B.C. And it came to a rather quick end in 400 B.C., most likely due because of war.
So if this super-ancient civilization has writings, that would go a long way in telling us more about them. Who were their kings? What were their modes of warfare? What was their size, physical characteristics and what happened to them? Were they destroyed or assimilated? How did they claim to get here?
If someone says a culture was here hundreds of thousands of years before other cultures, then I'm going to want more evidence than carbon dating. Civilizations cannot build cities and yet remain silent in the written word.