How to root eOS without TWRP?

depend on the device type, for some (like my old samsung s4) official instruction is to install the app from the store, then patch the boot.img include in the /e/OS.zip using the app, and flash it to the device.

without TWRP, it is possible using fastboot or for Samsung devices you can use heimdall, heimdall-front-end,thor, Odin3 windows, odin4linux or Galaxy-Flasher, the ultimate graphical tool for Samsung devices