Not a historian but a physician. Missing a period was/is the telltale sign of a suspected pregnancy, and it's pretty easy to calculate gestational age from there. There are also obvious physiological changes like the Chadwick's sign (bluish discolouration of the cervix and vagina), and Hegar's sign (softening of the cervix) that are present within 4-6 weeks of pregnancy. It is not far-fetched that non-modern cultures are able to estimate average lengths of gestation from these.

Not a historian but in the Mishana (which was written shortly after the destruction of the second temple 70CE). "pirkei avos" they list different things that corolate with the numbers 1-10. And it says that 9 is the length of pregnancy. Also in the Talmud it talks about the health of babies from 7 and 9 month long pregnancies. I'm on my phone now, so can't post exact quotes.

I'm not a historian either, but the traditional Chinese belief is that pregnancies last "10 months." I used to think the estimate was a bit long, but then somebody explained to me that it's talking about 10 months on the lunar calendar, which is 280 days.