This very much depends on one question: what kind of game would you like to make? If you really want to avoid any kind of programming, you would most likely have to find an engine that is preprogrammed specifically for the kind of game you want, and you may very likely find nothing like that in the FOSS world. I know how hard this is because my brother also wanted to make games without programming and he wasn't able to find anything good even in the proprietary world. And of course, without at least some programming you won't ever be able to create something truly nice, it's like wanting to write a book without knowing how to write.
A reasonable mid way can be creating a map/level in an existing game (e.g. Xonotic, OpenMW, ...). But to make the map really resemble a different game you'll need to write some simple scripts anyway.
I'd recommend learning a basic programming with
Pygame, it's a very simple 2D engine for which you need some simple knowledge of Python, but that's something you can perhaps learn in a few hours from their tutorials. It's an engine specifically made to be friendly to casual game makers.
If you want something even simpler, there is
Snap. It's something an elementary school student can handle, it has very simple visual programming, it runs in the browser and you can definitely make something like Flappy Bird in it.
EDIT:
Oh I see you want a 3D game, well that will be very difficult then. Best advice there I think is Godot then, but expect this to not be easy. There also used to be a 3D game engine in Blender (it's no longer there but you can still get the old version).