My hunch is that this is feasible. I haven't actually tried getting this to work, but...
You might be able to stop civs from reaching more advanced eras by editing the following file:
<Civ VI install folder>\Base\Assets\Gameplay\Data\Technologies.xml
There's also a "GameStartEra" option that controls the starting era of your game, and this lives in the following file:
<Civ VI install folder>\Base\Assets\Configuration\Data\SetupParameters.xml
So if you modded Technologies.xml not to have any eras after the Modern era, for example, and then you modded SetupParameters.xml to force the start era at Modern, then I believe you would get the modern-only game what you requested.