Or so the theory of relativity claims.
That theory was deduced through pure mathematics, not direct observation, as in classical physics. Most modern cosmology is based upon the works of Einstein and other theoretical mathematicians, and its explanations and predictions about the behavior and make-up of our universe show it.
Black holes, dark matter, quasars, expanding universe, the big bang, dark energy, pulsars, gravitational waves, etc., are all inventions proffered by mathematicians to paper over the glaring holes in the Standard Model.
But I digress.
The 250,000 year old figure for the age of Homo Sapiens was arrived at by using 20 years for each generation as a baseline. It's only an approximation, but I think it's close enough to make the case.
Just an aside to this discussion: while the theory was deduced through pure mathematics, the effect has been directly observed. One good example is the GPS satellite navigation system: to summarize, the entire thing works on VERY accurate clocks (atomic clocks with nanosecond accuracy). The high velocity of the satellites relative to the earth while (very much) below the speed of light, nonetheless introduces the predicted relativistic effects which are corrected using Einstein's equations.