From "Rhind Papyrus" from 1600 BC we know that the Egyptians had an estimate for $\pi$, namely 3.16, meaning they knew only 2 digits of $\pi$. According to this article they knew more digits, at least 4 digits of $\pi$. Around 200 BC Archimedes estimated pi to 22/7 which is 3 digits of $\pi$. This indicates that the Egyptians knew more digits 2000 years before Archimedes, however, it's not clear to me how many digits they actually knew.

<http://www.bcamt.ca/wp-content/uploads/2015/03/Yochim.pdf>