"They" knew it since the 3rd century BC and had a pretty good idea of its circumference since Eratosthenes' experiments.
Projections aren't needed to determine a position, angles to references and an as exact time as possible is enough, if you don't take into account for all of earth's orbital parameters, just the daily rotation.
Projections come when we want to draw a map(*), or for our applications, when we want to convert for instance the more intuitive spherical coordinates to Euclidian ones (x/y/z) for use in the computers. When I say I am at 28° North, 18° West that's much easier understand (provided you know where the 0-Meridian lies, or where you are in relation) than saying my UTM-position in WGS 84 is Zone 28R E: 216133.93 N: 3179691.71 (copied and pasted :-)). Or even what the renderer wants, a 3D-vector (5.33114e+06/-1.71164e+06/3.04494e+06).
:-)
(*) Fun fact: medieval and early modern times maps were east up so, that problem "what's up" is pretty old :-)