The Tathagata may have talked about different period of expansion of the Universe, it does not necessarily mean Our planet earth or this Expansion period after the Big Bang.
If i had heard The Tathagata say it i would not have any doubt. As I have not heard it from his lips, it is not impossible that it is somewhat skewed statement, but i think it is likely true as i have no reason to be inclined to doubt it.
However i also dont think it is the most useful thing to think about or a good way to verify the teaching.
Good ways to verify the teaching would be same you would verify any other theory:
a)cross referencing what is known as impossible and what is known as possible, ie putting theory against known legitimate experiements.
b)following instruction given in the teaching and verifying the experienced results vs the expected results
If you are not doing any of the above you are wasting time being skeptical or just lazy, complacent, perhaps it is pleasant to think about the theory and intellectually scrutinizing or poundering and reasoning, likely all of these but it is quite useless. At some point one has to say "ok i have enough evidence to set up a legit experiment", giving it a fair shot and collecting data from results.
It is not like one has to risk anything to undertake some precepts and do an intensive meditation course. It is all free and we are not the church of scientology, nobody will care much if you take or leave it.
The only concern is choosing the right teacher but that takes a certain skill and even for this we have teachings and manuals.
Humans are walking on this planet since 100000 years ago
I mean homo sapiens sapiens
more like 200 000 actually