So unfortunately the answer here is "Yes you can do it, but I probably wouldn't want to try".
At least on Windows, UE4 is really built around Visual Studio. It's possible to build project files for other IDEs, but support is limited, to say the least.
I think your best bet is to try to use the Linux Cross-Compiler, which I believe will force you into using GCC/Clang, but which does generate CMAKE or MAKE files. To enable this, you'll want to open up an existing project (or go digging in the engine INI files) and enable the plugin. The settings dropdown should have a button for "Plugins", and the one you want is in the "Programming" section. It's called "Linux Only Cross-Compiler" or something like that. Theoretically you can enable that and disable the Visual Studio integration plugin, which should do the trick.
You should then be able to find the .uproject file for a given project, right click it, and press "Generate Project Files" (or some other such button). For more info, check out the docs here
It's worth noting that you lose a lot of mostly valuable functionality this way though. The big one is that as slow as it is, intellisense is somewhat of a necessity when working in UE4 - the engine is practically built around the assumption that code/type completion is there to hold your hand.
Another downside is that there are plenty of weird bugs with the VS build system, and almost certainly some weirder ones with the linux/gcc build tools. When you have trouble, there will be zero existing support, and unfortunately, everyone you ask for help will say "go build it with VS and then come back".
So I'm fairly certain it's possible, if annoying
to set up; But don't let that stop you!