I'm looking at the 50th cousins, and wondering:
1st generation are siblings.
2nd are cousins.
3rd are 2nd cousins.
So to get to 50th cousins we'd need 50+1 generations. Allowing 25 years per generation, that's a measly 1,275 years. However, there's a big problem: This assumes each generation does not marry any kin, distant or otherwise. And that how far apart everyone would be from each other would depend on the population size.
Looking at it as the number of people required for each person to marry someone who isn't kin, and keeping this trimmed to two individuals in each generation, 2 siblings would need 2 people for a total of four. Next generation, 4 people needs 4 for a total of 16. Next generation, 8 people need eight people for a total of 64. So the totals are 2, 4, 16, 64, or 2^generation. Since 50th cousins need 51 generations, 2"51 = 2.2518x10^15. Over 2 quadrillion people at the level of the 51st generation. Current world population is 8.2 billion, or 8.2 x10^9. It's looking doubtful that anyone is even a 50th cousin.
If we go 2^X = 8.2x10^9: X*log2 = log(8.2x10^9); X = log(8.2X10^9)/log(2) = 32.933. Subtracting 1 from that and it's 31st to 32nd cousin at the most and most likely much closer than that, particularly given that marriage between couples who come from opposite sides of the globe wasn't even possible until the last few hundred years, and even then somewhat rare.
Just a very rough estimate, of course.