That's the basic disconnect between anthropology and linguistics. There's no evidence of modern man being around that long even using conventional dating schemes. To my knowledge, there's no evidence of caucasions being around more than about 10K or 12K years even using conventional schemes.
Moreover, the entire notion of language superfamilies such as nostratic is on very shaky ground. Many experts claim the similarities which comprise nostratic do not amount to more than you'd get by pure chance, i.e. they do not pass any sort of a null hypothesis test.
It's an area where we may never get much more evidence. I like the single-origin hypothesis simply because I suspect Homo erectus had some sort of primitive language by the time it diffused out of Africa.