Reddit user Xacius has the details on this tweak. Rename logos.bk2 to something else, and then either make a copy of WipeRight.bik and rename it logos.bk2 to replace the logos with a brief pattern, or (even better) download this blank bik video and use it instead. Instead, we have to replace it with a blank video. Unfortunately, just deleting logos.bk2 will cause Civ 6 to hang while loading.
Navigate to \Base\Platforms\Windows\Movies in the Civilization 6 install directory-see the fix above if you don't know where to look, or right click on the game in your Steam library, then select Properties > Local Files > Browse Local Files. The trick comes from Reddit account Civ6LogoSkip, which is a very specific account to have, but a very useful one to us. It's easy to disable the main intro video-it's in the options menu, under 'Application'-but also getting rid of the logo splash screens is slightly trickier.