Hi. It’s hard to put an exact date on when modern humans (Homo Sapians) evolved due to the limited information in the fossil record, but it is probably in the region of 250,000 years ago. For context, the Earth is about 4.5 billion years old, so humans have only been around for a tiny fraction of the lifetime of the Earth!
Life expectancy has changed a lot over that time due to better healthcare and our ability to provide shelter for ourselves and a decrease in the number of predators, but we could maybe say that the average life expectancy is about 40 years. Therefore, there will have been about 6000 generations before us!
There were also many other earlier humanoid species like Homo habilis that were around 2 million years ago, but these were more like chimps.
As Greig has said, it depends on various things. The first modern human was probably around about 250,000 years ago, but then it doesn’t matter what the life expectancy was/is just at what age your ancestors had children. Most animals start having children as soon as they are ready and able, so I don’t think early humans would have been very different. So, I’ll say that on average, in the history of all humans, people were born when their parents were about 16 (some will have been born to even younger parents, but some to older parents too, so hopefully the average will work). That would put the number of Greats as 15625!
Just like Greig explained, the first modern humans walked the Earth sometime around 250 000 years ago (but it’s hard to tell, definitely before 200 000 years ago.) Then it’s just a matter of knowing the average age of reproduction of humans (specifically women) as a function of time.
(As a side note : life expectancy isn’t a good thing to look at because it included children mortality, so people who died before they could have a chance to reproduce, and those are definitely not our ancestors. Surprisingly even until the mid 1850s, out of a family of 6 children only about 4 would make it to adulthood – almost a third would die before the age of 5 – that’s why families were SO big bak then).
So human lifespan (which is how long an individual who makes it to adulthood can expect to live) didn’t pass 30 until about 30 000 years ago. But the fertility age is a bit harder to figure out. Using data from the 1850s (again), girls used to have their first periods on average around 17 to 15 years old (much later than today!!) depending on the country. So we can probably safely assume that for most of the history of humanity, women had their babies at around 20 (on average: some before, some after).
That would make 12 500 generations since the dawn of modern humans. That’s a lot !